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zHdY57Fy_IYz>MG|)o05ixSttQ6|ZNM`-D~i(?&=tVPM8NmShKVmBEk;OxQNZ{PrMq zT?Tk?P-E0VmrST~PyrHF*}uX3^o(k_42NT^rnbq(Xa%r9p7QV#faDDrHvy+~LkZeYb(k^*b0-TJ$EQ!9#=&dQgx@m3=r8yd z?Be$Fpd-##9NLEQK3JhiJ`5QVtjOUeFDNLe^T(}wXc7_qWo0Gu-Q8h=14fKOBkj@X zDR8~i^38=TkVra!;zRw^^k)^h0z)wFPz?^k6TqxAg_uX7COu1rzW25_mYy408#P4> oX&lq>mF?fv)lifEcSW}ipQuP{hO(B7pK3h*(lz/dev/null 2>/dev/null\n", - " !pip install highspy >/dev/null 2>/dev/null\n", - "\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('appsi_highs')\n", - " \n", - "else:\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('cbc')\n", - "\n", - "assert SOLVER.available(), f\"Solver {SOLVER} is not available.\"" + " %pip install pyomo >/dev/null 2>/dev/null\n", + " %pip install highspy >/dev/null 2>/dev/null\n", + " \n", + "solver = 'appsi_highs'\n", + " \n", + "import pyomo.environ as pyo\n", + "SOLVER = pyo.SolverFactory(solver)\n", + " \n", + "assert SOLVER.available(), f\"Solver {solver} is not available.\"" ] }, { @@ -332,8 +325,6 @@ "metadata": {}, "outputs": [], "source": [ - "import pyomo.environ as pyo\n", - "\n", "model = pyo.ConcreteModel()" ] }, @@ -552,6 +543,8 @@ " labor B : -Inf : 2*y[U] + y[V] - x[labor B] : 0.0 : True\n", "\n", "12 Declarations: PRODUCTS RESOURCES demand available cp cr a_index a x y profit materials_used\n", + "Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]\n", + "Copyright (c) 2023 HiGHS under MIT licence terms\n", "Profit = 2600.0\n", "\n", "Production Report\n", @@ -601,6 +594,8 @@ "name": "stdout", "output_type": "stream", "text": [ + "Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]\n", + "Copyright (c) 2023 HiGHS under MIT licence terms\n", "Profit = 2600.0\n", "\n", "Production Report\n", @@ -615,9 +610,6 @@ } ], "source": [ - "import pyomo.environ as pyo\n", - "\n", - "\n", "class ProductionModel(pyo.ConcreteModel):\n", " \"\"\"\n", " A class representing a production model using Pyomo.\n", @@ -736,7 +728,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.2" + "version": "3.10.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/_sources/notebooks/01/production-planning-basic.ipynb b/_sources/notebooks/01/production-planning-basic.ipynb index 33373119..6c19bcd3 100644 --- a/_sources/notebooks/01/production-planning-basic.ipynb +++ b/_sources/notebooks/01/production-planning-basic.ipynb @@ -16,7 +16,7 @@ "```\n", "```{index} single: Pyomo; decorators\n", "```\n", - "```{index} single: solver; cbc\n", + "```{index} single: solver; HiGHS\n", "```\n", "\n", "# A basic Pyomo model\n", @@ -42,14 +42,17 @@ "source": [ "## Preamble: Install Pyomo and a solver\n", "\n", - "This collection of notebooks is intended to be run in the cloud on [Google Colab](https://colab.google/) or on a personal computer. To meet this goal, we start each notebook by verifying the installation of Pyomo and an appropriate solver. When run on Google Colab, an installation of Pyomo and a solver must be done for each new Colab session. The [HiGHS solver](https://highs.dev/) is a high performance open source solver for linear and mixed integer optimization on Google Colab. For a personal computer, we assume Python, Pyomo and the [COIN-OR Cbc solver](https://coin-or.github.io/Cbc/intro.html) (\"COIN-OR branch and cut\") have been previously installed. Note that there are other suitable solvers, both open-source, such as GLPK, and commercial, such as CPLEX, Gurobi, and Mosek.\n", + "This collection of notebooks is intended to be run in the cloud on [Google Colab](https://colab.google/) or on a personal computer. To meet this goal, we start each notebook by verifying the installation of Pyomo and an appropriate solver. \n", "\n", - "The following cell checks if the notebook is running on Google Colab. If so, it does a quiet installation of Pyomo and a solver. A solver is then selected, a test performed to verify that the solver is available, and the solver interface is stored in a global object `SOLVER` for later use." + "When run on Google Colab, an installation of Pyomo and a solver must be done for each new Colab session. The [HiGHS solver](https://highs.dev/) is a high performance open source solver for linear and mixed integer optimization on Google Colab. For a personal computer, we assume Python, Pyomo and the [HiGHS solver](https://highs.dev/) have been previously installed. Note that there are other suitable solvers, both open-source, such as [COIN-OR Cbc solver](https://coin-or.github.io/Cbc/intro.html) and [GLPK](https://www.gnu.org/software/glpk/), and commercial, such as CPLEX, Gurobi, and Mosek.\n", + "\n", + "The following cell sets and verifies a global SOLVER for the notebook. If run on Google Colab, the cell installs Pyomo and the HiGHS solver, while, if run elsewhere, it \n", + "assumes Pyomo and HiGHS have been previously installed. It then sets to use HiGHS as solver via the appsi module and a test is performed to verify that it is available. The solver interface is stored in a global object `SOLVER` for later use." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -70,29 +73,18 @@ }, "outputs": [], "source": [ - "\"\"\"\n", - "This cell sets and verifies a global SOLVER for the notebook.\n", - "\n", - "If run on Google Colab, the cell installs Pyomo and HiGHS, then sets SOLVER to use\n", - "the Highs solver via the appsi module. If run elsewhere, it assumes Pyomo and CBC\n", - "have been previously installed and sets SOLVER to use the CBC solver via the Pyomo \n", - "SolverFactory. For both cases, it then verifies that SOLVER is available.\n", - "\"\"\"\n", - "\n", "import sys\n", - "\n", + " \n", "if 'google.colab' in sys.modules:\n", - " !pip install pyomo >/dev/null 2>/dev/null\n", - " !pip install highspy >/dev/null 2>/dev/null\n", - "\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('appsi_highs')\n", - " \n", - "else:\n", - " from pyomo.environ import SolverFactory\n", - " SOLVER = SolverFactory('cbc')\n", - "\n", - "assert SOLVER.available(), f\"Solver {SOLVER} is not available.\"" + " %pip install pyomo >/dev/null 2>/dev/null\n", + " %pip install highspy >/dev/null 2>/dev/null\n", + " \n", + "solver = 'appsi_highs'\n", + " \n", + "import pyomo.environ as pyo\n", + "SOLVER = pyo.SolverFactory(solver)\n", + " \n", + "assert SOLVER.available(), f\"Solver {solver} is not available.\"" ] }, { @@ -101,12 +93,12 @@ "source": [ "## Step 1. Import Pyomo\n", "\n", - "The first step for a new Pyomo model is to import the needed components into the Python environment. The module `pyomo.environ` provides the components most commonly used for building Pyomo models. This collection of notebooks uses a consistent convention of importing `pyomo.environ` with the `pyo` prefix." + "The first step for a new Pyomo model is to import the needed components into the Python environment. The module `pyomo.environ` provides the components most commonly used for building Pyomo models. Although this module was imported in the previous code cell, we mention it again here also to emphasize our standardized conventions. Throughout this collection of notebooks, a uniform standard is maintained for importing `pyomo.environ` consistently using the alias `pyo`." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "tags": [] }, @@ -128,7 +120,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "tags": [] }, @@ -147,7 +139,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -191,7 +183,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "tags": [] }, @@ -251,7 +243,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { "tags": [] }, @@ -286,75 +278,30 @@ "The first method is to use `pyo.Objective()` where the expression to be optimized is assigned with the `expr` keyword and the type of objective is assigned with the `sense` keyword.\n", "\n", "```python\n", - " model.profit = pyo.Objective(expr = model.revenue - model.cost, sense = pyo.maximize)\n", + " model.profit = pyo.Objective(expr=model.revenue - model.cost, sense=pyo.maximize)\n", "```\n", - " \n", - "Recent releases of Pyomo provide a second method that uses Python [decorators](https://peps.python.org/pep-0318/) to specify an objective. With a decorator, the same objective is written as\n", - "\n", - "```python\n", - " @model.Objective(sense = pyo.maximize)\n", - " def profit(m):\n", - " return m.revenue - m.cost\n", - "```\n", - "\n", - "Python decorators modify the behavior of the function defined in the next line. In this case, the decorator `@model.Objective()` modifies the behavior of `profit()` so that it returns an expression for the profit to Pyomo. The keyword `sense` sets the type of objective, which can either be to maximize or minimize the value returned by the objective function. The function `profit()`, after being decorated, takes the Pyomo model as its first argument and adds its name to the model attributes.\n", "\n", - "In effect, Pyomo decorators are tags that insert functions into a Pyomo model to serve as expressions, objectives, or constraints. Decorators can improve the readability and maintainability of more complex models. They also simplify the syntax for creating other Pyomo objects expressions, constraints, and other optimization-related elements." + "Recent releases of Pyomo provide a second method that uses Python [decorators](https://peps.python.org/pep-0318/) to specify an objective. With a decorator, the same objective is written as" ] }, { "cell_type": "code", - "execution_count": 8, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Model 'Production Planning: Version 1'\n", - "\n", - " Variables:\n", - " x_M : Size=1, Index=None\n", - " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", - " None : 0 : None : None : False : True : Reals\n", - " x_A : Size=1, Index=None\n", - " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", - " None : 0 : None : 80 : False : True : Reals\n", - " x_B : Size=1, Index=None\n", - " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", - " None : 0 : None : 100 : False : True : Reals\n", - " y_U : Size=1, Index=None\n", - " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", - " None : 0 : None : 40 : False : True : Reals\n", - " y_V : Size=1, Index=None\n", - " Key : Lower : Value : Upper : Fixed : Stale : Domain\n", - " None : 0 : None : None : False : True : Reals\n", - "\n", - " Objectives:\n", - " profit : Size=1, Index=None, Active=True\n", - "ERROR: evaluating object as numeric value: y_U\n", - " (object: )\n", - " No value for uninitialized NumericValue object y_U\n", - "ERROR: evaluating object as numeric value: profit\n", - " (object: )\n", - " No value for uninitialized NumericValue object y_U\n", - " Key : Active : Value\n", - " None : None : None\n", - "\n", - " Constraints:\n", - " None\n" - ] - } - ], + "execution_count": 7, + "metadata": {}, + "outputs": [], "source": [ "@model.Objective(sense=pyo.maximize)\n", "def profit(m):\n", - " return m.revenue - m.cost\n", - "\n", + " return m.revenue - m.cost" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Python decorators modify the behavior of the function defined in the next line. In this case, the decorator `@model.Objective()` modifies the behavior of `profit()` so that it returns an expression for the profit to Pyomo. The keyword `sense` sets the type of objective, which can either be to maximize or minimize the value returned by the objective function. The function `profit()`, after being decorated, takes the Pyomo model as its first argument and adds its name to the model attributes.\n", "\n", - "model.display()" + "In effect, Pyomo decorators are tags that insert functions into a Pyomo model to serve as expressions, objectives, or constraints. Decorators can improve the readability and maintainability of more complex models. They also simplify the syntax for creating other Pyomo objects expressions, constraints, and other optimization-related elements." ] }, { @@ -367,16 +314,18 @@ "\n", "Constraints can be created with `pyo.Constraint()`. The constraint is passed as a keyword argument `expr` to `pyo.Constraint()`. For this application the constraints could be expressed as \n", "\n", + "```python\n", " model.raw_materials = pyo.Constraint(expr = 10 * model.y_U + 9 * model.y_V <= model.x_M)\n", " model.labor_A = pyo.Constraint(expr = 1 * model.y_U + 1 * model.y_V <= model.x_A)\n", " model.labor_B = pyo.Constraint(expr = 2 * model.y_U + 1 * model.y_V <= model.x_B)\n", + "```\n", " \n", "Alternatively, the `@model.Constraint()` decorator 'tags' the output of the following function as a constraint. For the present example, the constraints are expressed with decorators below. This collection of notebooks uses decorators whenever possible to improve the readability and maintainability of Pyomo models." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": { "tags": [] }, @@ -452,7 +401,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": { "tags": [] }, @@ -461,38 +410,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.10 \n", - "Build Date: Apr 20 2023 \n", - "\n", - "command line - /opt/homebrew/opt/cbc/bin/cbc -printingOptions all -import /var/folders/zb/k0pc77yj6c3gv6gr6jj41g1r0000gn/T/tmp2_hwem4f.pyomo.lp -stat=1 -solve -solu /var/folders/zb/k0pc77yj6c3gv6gr6jj41g1r0000gn/T/tmp2_hwem4f.pyomo.soln (default strategy 1)\n", - "Option for printingOptions changed from normal to all\n", - " CoinLpIO::readLp(): Maximization problem reformulated as minimization\n", - "Coin0009I Switching back to maximization to get correct duals etc\n", - "Presolve 3 (0) rows, 5 (0) columns and 9 (0) elements\n", - "Statistics for presolved model\n", - "\n", - "\n", - "Problem has 3 rows, 5 columns (5 with objective) and 9 elements\n", - "There are 3 singletons with objective \n", - "Column breakdown:\n", - "2 of type 0.0->inf, 3 of type 0.0->up, 0 of type lo->inf, \n", - "0 of type lo->up, 0 of type free, 0 of type fixed, \n", - "0 of type -inf->0.0, 0 of type -inf->up, 0 of type 0.0->1.0 \n", - "Row breakdown:\n", - "2 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", - "0 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", - "0 of type G other, 1 of type L 0.0, 0 of type L 1.0, \n", - "0 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", - "0 of type Free \n", - "Presolve 3 (0) rows, 5 (0) columns and 9 (0) elements\n", - "0 Obj 0 Dual inf 480 (2)\n", - "0 Obj 0 Dual inf 480 (2)\n", - "6 Obj 2600\n", - "Optimal - objective value 2600\n", - "Optimal objective 2600 - 6 iterations time 0.002\n", - "Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00\n", - "\n" + "Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]\n", + "Copyright (c) 2023 HiGHS under MIT licence terms\n", + "WARNING: No semi-integer/integer variables in model with non-empty integrality\n", + "Presolving model\n", + "2 rows, 4 cols, 6 nonzeros\n", + "2 rows, 4 cols, 6 nonzeros\n", + "Presolve : Reductions: rows 2(-1); columns 4(-1); elements 6(-3)\n", + "Solving the presolved LP\n", + "Using EKK dual simplex solver - serial\n", + " Iteration Objective Infeasibilities num(sum)\n", + " 0 -2.0999953995e+02 Ph1: 2(4); Du: 3(210) 0s\n", + " 3 -2.6000000000e+03 Pr: 0(0) 0s\n", + "Solving the original LP from the solution after postsolve\n", + "Model status : Optimal\n", + "Simplex iterations: 3\n", + "Objective value : 2.6000000000e+03\n", + "HiGHS run time : 0.00\n" ] } ], @@ -520,7 +454,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -571,7 +505,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -600,7 +534,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -609,7 +543,7 @@ "2600.0" ] }, - "execution_count": 13, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -627,7 +561,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -655,7 +589,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -685,7 +619,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -738,12 +672,12 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -800,7 +734,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.2" + "version": "3.10.10" }, "latex_envs": { "LaTeX_envs_menu_present": true, diff --git a/genindex.html b/genindex.html index aa53d7ab..0cfcecc0 100644 --- a/genindex.html +++ b/genindex.html @@ -671,11 +671,13 @@

S

solver
    -
  • cbc, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31] +
  • cbc, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30]
  • cplex, [1], [2]
  • cvxpy +
    • +
  • HiGHS
  • highs, [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]
    • diff --git a/notebooks/01/production-planning-advanced.html b/notebooks/01/production-planning-advanced.html index 60ca3732..00bbe780 100644 --- a/notebooks/01/production-planning-advanced.html +++ b/notebooks/01/production-planning-advanced.html @@ -529,27 +529,21 @@

    Contents

    We will begin this analysis by examining the problem data sets to identify the underlying problem structure.

    Preamble: Install Pyomo and a solver#

    -

    This cell selects and verifies a global SOLVER for the notebook.

    -

    If run on Google Colab, the cell installs Pyomo and HiGHS, then sets SOLVER to -use the Highs solver via the appsi module. If run elsewhere, it assumes Pyomo and CBC -have been previously installed and sets SOLVER to use the CBC solver via the Pyomo -SolverFactory. It then verifies that SOLVER is available.

    +

    The following cell checks if the notebook is run on Google Colab. If so, it does a quiet installation of Pyomo and the HiGHS solver. The solver is then selected, a test performed to verify that the solver is available, and the solver interface is stored in a global object SOLVER for later use.

    import sys
-
+ 
 if 'google.colab' in sys.modules:
-    !pip install pyomo >/dev/null 2>/dev/null
-    !pip install highspy >/dev/null 2>/dev/null
-
-    from pyomo.environ import SolverFactory
-    SOLVER = SolverFactory('appsi_highs')
-    
-else:
-    from pyomo.environ import SolverFactory
-    SOLVER = SolverFactory('cbc')
-
-assert SOLVER.available(), f"Solver {SOLVER} is not available."
+    %pip install pyomo >/dev/null 2>/dev/null
+    %pip install highspy >/dev/null 2>/dev/null
+ 
+solver = 'appsi_highs'
+ 
+import pyomo.environ as pyo
+SOLVER = pyo.SolverFactory(solver)
+ 
+assert SOLVER.available(), f"Solver {solver} is not available."
    @@ -813,9 +807,7 @@

    The production model in PyomoConcreteModel.

    -
    import pyomo.environ as pyo
-
-model = pyo.ConcreteModel()
+
    model = pyo.ConcreteModel()
    @@ -998,6 +990,8 @@

    The production model in PyomoSome readers of these notebooks may be more experienced Python developers who wish to apply Pyomo in more specialized, data driven applications. The following cell shows how the Pyomo ConcreteModel() class can be extended by subclassing to create specialized model classes. Here we create a subclass called ProductionModel that accepts a particular representation of the problem data to produce a production model object. The production model object inherits all of the methods associated with any ConcreteModel, such as .display(), .solve(), and .pprint(), but can be extended with additional methods.

    -
    import pyomo.environ as pyo
-
-
-class ProductionModel(pyo.ConcreteModel):
+
    class ProductionModel(pyo.ConcreteModel):
     """
     A class representing a production model using Pyomo.
     """
@@ -1120,7 +1111,9 @@ 
    For Python experts: Creating subclasses of 
-
    Profit = 2600.0
+
    Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]
+Copyright (c) 2023 HiGHS under MIT licence terms
+Profit = 2600.0
 
 Production Report
  U  produced =  20.0
diff --git a/notebooks/01/production-planning-basic.html b/notebooks/01/production-planning-basic.html
index 71a62928..5e482c99 100644
--- a/notebooks/01/production-planning-basic.html
+++ b/notebooks/01/production-planning-basic.html
@@ -539,33 +539,24 @@ 
     Contents 
    
 
    This notebook also introduces the use of Python decorators to designate Pyomo expressions, objectives, and constraints. While decorators may be unfamiliar to some Python users, or even current Pyomo users, they offer a significant improvement in the readability of Pyomo model. This feature is relatively new and is available in recent versions of Pyomo.
    
 
    
 
    Preamble: Install Pyomo and a solver#
    
-
    This collection of notebooks is intended to be run in the cloud on Google Colab or on a personal computer. To meet this goal, we start each notebook by verifying the installation of Pyomo and an appropriate solver. When run on Google Colab, an installation of Pyomo and a solver must be done for each new Colab session. The HiGHS solver is a high performance open source solver for linear and mixed integer optimization on Google Colab.  For a personal computer, we assume Python, Pyomo and the COIN-OR Cbc solver (“COIN-OR branch and cut”) have been previously installed. Note that there are other suitable solvers, both open-source, such as GLPK, and commercial, such as CPLEX, Gurobi, and Mosek.
    
-
    The following cell checks if the notebook is running on Google Colab. If so, it does a quiet installation of Pyomo and a solver. A solver is then selected, a test performed to verify that the solver is available, and the solver interface is stored in a global object SOLVER for later use.
    
+
    This collection of notebooks is intended to be run in the cloud on Google Colab or on a personal computer. To meet this goal, we start each notebook by verifying the installation of Pyomo and an appropriate solver.
    
+
    When run on Google Colab, an installation of Pyomo and a solver must be done for each new Colab session. The HiGHS solver is a high performance open source solver for linear and mixed integer optimization on Google Colab. For a personal computer, we assume Python, Pyomo and the HiGHS solver have been previously installed. Note that there are other suitable solvers, both open-source, such as COIN-OR Cbc solver and GLPK, and commercial, such as CPLEX, Gurobi, and Mosek.
    
+
    The following cell sets and verifies a global SOLVER for the notebook. If run on Google Colab, the cell installs Pyomo and the HiGHS solver, while, if run elsewhere, it
+assumes Pyomo and HiGHS have been previously installed. It then sets to use HiGHS as solver via the appsi module and a test is performed to verify that it is available. The solver interface is stored in a global object SOLVER for later use.
    
 
    
 
    
-
    """
-This cell sets and verifies a global SOLVER for the notebook.
-
-If run on Google Colab, the cell installs Pyomo and HiGHS, then sets SOLVER to use
-the Highs solver via the appsi module. If run elsewhere, it assumes Pyomo and CBC
-have been previously installed and sets SOLVER to use the CBC solver via the Pyomo 
-SolverFactory. For both cases, it then verifies that SOLVER is available.
-"""
-
-import sys
-
+
    import sys
+ 
 if 'google.colab' in sys.modules:
-    !pip install pyomo >/dev/null 2>/dev/null
-    !pip install highspy >/dev/null 2>/dev/null
-
-    from pyomo.environ import SolverFactory
-    SOLVER = SolverFactory('appsi_highs')
-    
-else:
-    from pyomo.environ import SolverFactory
-    SOLVER = SolverFactory('cbc')
-
-assert SOLVER.available(), f"Solver {SOLVER} is not available."
+    %pip install pyomo >/dev/null 2>/dev/null
+    %pip install highspy >/dev/null 2>/dev/null
+ 
+solver = 'appsi_highs'
+ 
+import pyomo.environ as pyo
+SOLVER = pyo.SolverFactory(solver)
+ 
+assert SOLVER.available(), f"Solver {solver} is not available."
 
    
 
    
 
    
@@ -573,7 +564,7 @@ 
    Preamble: Install Pyomo and a solver
 
    Step 1. Import Pyomo#
    
-
    The first step for a new Pyomo model is to import the needed components into the Python environment. The module pyomo.environ provides the components most commonly used for building Pyomo models. This collection of notebooks uses a consistent convention of importing pyomo.environ with the pyo prefix.
    
+
    The first step for a new Pyomo model is to import the needed components into the Python environment. The module pyomo.environ provides the components most commonly used for building Pyomo models. Although this module was imported in the previous code cell, we mention it again here also to emphasize our standardized conventions. Throughout this collection of notebooks, a uniform standard is maintained for importing pyomo.environ consistently using the alias pyo.
    
 
    
 
    
 
    import pyomo.environ as pyo
@@ -699,73 +690,29 @@ 
    Step 4. Expressions#
    
 
    The objective for this example is to maximize profit which is given by the difference between revenue and cost. There are two ways this objective could be specified in Pyomo.
    
 
    The first method is to use pyo.Objective() where the expression to be optimized is assigned with the expr keyword and the type of objective is assigned with the sense keyword.
    
-
        model.profit = pyo.Objective(expr = model.revenue - model.cost, sense = pyo.maximize)
+
        model.profit = pyo.Objective(expr=model.revenue - model.cost, sense=pyo.maximize)
 
    
 
    
 
    Recent releases of Pyomo provide a second method that uses Python decorators to specify an objective. With a decorator, the same objective is written as
    
-
        @model.Objective(sense = pyo.maximize)
-    def profit(m):
-        return m.revenue - m.cost
-
    
-
    
-
    Python decorators modify the behavior of the function defined in the next line.  In this case, the decorator @model.Objective() modifies the behavior of profit() so that it returns an expression for the profit to Pyomo. The keyword sense sets the type of objective, which can either be to maximize or minimize the value returned by the objective function. The function profit(), after being decorated, takes the Pyomo model as its first argument and adds its name to the model attributes.
    
-
    In effect, Pyomo decorators are tags that insert functions into a Pyomo model to serve as expressions, objectives, or constraints. Decorators can improve the readability and maintainability of more complex models. They also simplify the syntax for creating other Pyomo objects expressions, constraints, and other optimization-related elements.
    
 
    
 
    
 
    @model.Objective(sense=pyo.maximize)
 def profit(m):
     return m.revenue - m.cost
-
-
-model.display()
-
    
-
    
-
    
-
    
-
    Model 'Production Planning: Version 1'
-
-  Variables:
-    x_M : Size=1, Index=None
-        Key  : Lower : Value : Upper : Fixed : Stale : Domain
-        None :     0 :  None :  None : False :  True :  Reals
-    x_A : Size=1, Index=None
-        Key  : Lower : Value : Upper : Fixed : Stale : Domain
-        None :     0 :  None :    80 : False :  True :  Reals
-    x_B : Size=1, Index=None
-        Key  : Lower : Value : Upper : Fixed : Stale : Domain
-        None :     0 :  None :   100 : False :  True :  Reals
-    y_U : Size=1, Index=None
-        Key  : Lower : Value : Upper : Fixed : Stale : Domain
-        None :     0 :  None :    40 : False :  True :  Reals
-    y_V : Size=1, Index=None
-        Key  : Lower : Value : Upper : Fixed : Stale : Domain
-        None :     0 :  None :  None : False :  True :  Reals
-
-  Objectives:
-    profit : Size=1, Index=None, Active=True
-ERROR: evaluating object as numeric value: y_U
-        (object: <class 'pyomo.core.base.var.ScalarVar'>)
-    No value for uninitialized NumericValue object y_U
-ERROR: evaluating object as numeric value: profit
-        (object: <class 'pyomo.core.base.objective.ScalarObjective'>)
-    No value for uninitialized NumericValue object y_U
-        Key : Active : Value
-        None :   None :  None
-
-  Constraints:
-    None
 
    
 
    
 
    
 
    
+
    Python decorators modify the behavior of the function defined in the next line.  In this case, the decorator @model.Objective() modifies the behavior of profit() so that it returns an expression for the profit to Pyomo. The keyword sense sets the type of objective, which can either be to maximize or minimize the value returned by the objective function. The function profit(), after being decorated, takes the Pyomo model as its first argument and adds its name to the model attributes.
    
+
    In effect, Pyomo decorators are tags that insert functions into a Pyomo model to serve as expressions, objectives, or constraints. Decorators can improve the readability and maintainability of more complex models. They also simplify the syntax for creating other Pyomo objects expressions, constraints, and other optimization-related elements.
    
 
    
 
    
 
    Step 6. Constraints#
    
 
    Constraints are logical relationships between expressions that define the range of feasible solutions in an optimization problem. A constraint consists of two expressions separated by one of the logical relationships. The logical relationships can be equality (==), less-than (<=), or greater-than (>=).
    
 
    Constraints can be created with pyo.Constraint(). The constraint is passed as a keyword argument expr to pyo.Constraint(). For this application the constraints could be expressed as
    
-
    model.raw_materials = pyo.Constraint(expr = 10 * model.y_U + 9 * model.y_V <= model.x_M)
-model.labor_A = pyo.Constraint(expr = 1 * model.y_U + 1 * model.y_V <= model.x_A)
-model.labor_B = pyo.Constraint(expr = 2 * model.y_U + 1 * model.y_V <= model.x_B)
+
        model.raw_materials = pyo.Constraint(expr = 10 * model.y_U + 9 * model.y_V <= model.x_M)
+    model.labor_A = pyo.Constraint(expr = 1 * model.y_U + 1 * model.y_V <= model.x_A)
+    model.labor_B = pyo.Constraint(expr = 2 * model.y_U + 1 * model.y_V <= model.x_B)
 
    
 
    
 
    Alternatively, the @model.Constraint() decorator ‘tags’ the output of the following function as a constraint. For the present example, the constraints are expressed with decorators below. This collection of notebooks uses decorators whenever possible to improve the readability and maintainability of Pyomo models.
    
@@ -840,37 +787,23 @@ 
    Step 7. Solve the model
 
    
 
    
-
    Welcome to the CBC MILP Solver 
-Version: 2.10.10 
-Build Date: Apr 20 2023 
-
-command line - /opt/homebrew/opt/cbc/bin/cbc -printingOptions all -import /var/folders/zb/k0pc77yj6c3gv6gr6jj41g1r0000gn/T/tmp2_hwem4f.pyomo.lp -stat=1 -solve -solu /var/folders/zb/k0pc77yj6c3gv6gr6jj41g1r0000gn/T/tmp2_hwem4f.pyomo.soln (default strategy 1)
-Option for printingOptions changed from normal to all
- CoinLpIO::readLp(): Maximization problem reformulated as minimization
-Coin0009I Switching back to maximization to get correct duals etc
-Presolve 3 (0) rows, 5 (0) columns and 9 (0) elements
-Statistics for presolved model
-
-
-Problem has 3 rows, 5 columns (5 with objective) and 9 elements
-There are 3 singletons with objective 
-Column breakdown:
-2 of type 0.0->inf, 3 of type 0.0->up, 0 of type lo->inf, 
-0 of type lo->up, 0 of type free, 0 of type fixed, 
-0 of type -inf->0.0, 0 of type -inf->up, 0 of type 0.0->1.0 
-Row breakdown:
-2 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, 
-0 of type E other, 0 of type G 0.0, 0 of type G 1.0, 
-0 of type G other, 1 of type L 0.0, 0 of type L 1.0, 
-0 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, 
-0 of type Free 
-Presolve 3 (0) rows, 5 (0) columns and 9 (0) elements
-0  Obj 0 Dual inf 480 (2)
-0  Obj 0 Dual inf 480 (2)
-6  Obj 2600
-Optimal - objective value 2600
-Optimal objective 2600 - 6 iterations time 0.002
-Total time (CPU seconds):       0.00   (Wallclock seconds):       0.00
+
    Running HiGHS 1.5.3 [date: 2023-05-16, git hash: 594fa5a9d]
+Copyright (c) 2023 HiGHS under MIT licence terms
+WARNING: No semi-integer/integer variables in model with non-empty integrality
+Presolving model
+2 rows, 4 cols, 6 nonzeros
+2 rows, 4 cols, 6 nonzeros
+Presolve : Reductions: rows 2(-1); columns 4(-1); elements 6(-3)
+Solving the presolved LP
+Using EKK dual simplex solver - serial
+  Iteration        Objective     Infeasibilities num(sum)
+          0    -2.0999953995e+02 Ph1: 2(4); Du: 3(210) 0s
+          3    -2.6000000000e+03 Pr: 0(0) 0s
+Solving the original LP from the solution after postsolve
+Model   status      : Optimal
+Simplex   iterations: 3
+Objective value     :  2.6000000000e+03
+HiGHS run time      :          0.00
 
    
 
    
 
    
@@ -1060,7 +993,7 @@ 
    Creating reports with Pandas
-../../_images/cc4837d53cfd8491d2d7eac3d54a65e8f1ba9d94ac68084f404622a417d7b106.png
+../../_images/bbf21b7015cc83ed41ea77948f1b50e50acb157c2ec5cec3589d2e68f557b116.png
 
    
 
    
 
    To discover more advanced Pyomo features, see the next notebook.
    
diff --git a/searchindex.js b/searchindex.js
index ad9e70b3..31881a00 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["genindex", "intro", "notebooks/01/01.00", "notebooks/01/production-planning", "notebooks/01/production-planning-advanced", "notebooks/01/production-planning-basic", "notebooks/02/02.00", "notebooks/02/L1-regression-wine-quality", "notebooks/02/bim", "notebooks/02/bim-dual", "notebooks/02/bim-fractional", "notebooks/02/bim-maxmin", "notebooks/02/bim-rawmaterialplanning", "notebooks/02/lad-regression", "notebooks/02/mad-portfolio-optimization", "notebooks/02/multiproductionfaciliity_worstcase", "notebooks/03/03.00", "notebooks/03/bim-perturbed", "notebooks/03/bim-production-revisited", "notebooks/03/cryptarithms", "notebooks/03/facility-location", "notebooks/03/job-shop-scheduling", "notebooks/03/machine-scheduling", "notebooks/03/maintenance-planning", "notebooks/03/recharging-electric-vehicle", "notebooks/03/shift-scheduling", "notebooks/03/simple-production-model-gdp", "notebooks/03/strip-packing", "notebooks/04/04.00", "notebooks/04/cryptocurrency-arbitrage", "notebooks/04/dinner-seat-allocation", "notebooks/04/forex-arbitrage", "notebooks/04/gasoline-distribution", "notebooks/04/graph-coloring", "notebooks/04/mincost-flow", "notebooks/04/power-network", "notebooks/05/05.00", "notebooks/05/cutting-stock", "notebooks/05/markowitz_portfolio", "notebooks/05/milk-pooling", "notebooks/05/ols-regression", "notebooks/05/refinery-production", "notebooks/05/svm", "notebooks/06/06.00", "notebooks/06/building-insulation", "notebooks/06/economic-order-quantity", "notebooks/06/investment-wheel", "notebooks/06/kelly-criterion", "notebooks/06/markowitz_portfolio_revisited", "notebooks/06/optimal-growth-portfolios", "notebooks/06/svm-conic", "notebooks/07/07.00", "notebooks/07/bim-robustness-analysis", "notebooks/07/fleet-assignment", "notebooks/08/08.00", "notebooks/08/bim-robust-optimization", "notebooks/09/09.00", "notebooks/09/economicdispatch", "notebooks/09/markowitz_portfolio_with_chance_constraint", "notebooks/09/pop-up_shop", "notebooks/09/seafood", "notebooks/10/10.00", "notebooks/10/airline-seating", "notebooks/10/ccg", "notebooks/10/farmer", "notebooks/10/opf-ldr", "notebooks/10/opf-wind-curtailment", "notebooks/appendix/appendix", "notebooks/appendix/functional-programming-pyomo", "notebooks/appendix/pyomo-style-guide"], "filenames": ["genindex.md", "intro.md", "notebooks/01/01.00.md", "notebooks/01/production-planning.ipynb", "notebooks/01/production-planning-advanced.ipynb", "notebooks/01/production-planning-basic.ipynb", "notebooks/02/02.00.md", "notebooks/02/L1-regression-wine-quality.ipynb", "notebooks/02/bim.ipynb", "notebooks/02/bim-dual.ipynb", "notebooks/02/bim-fractional.ipynb", "notebooks/02/bim-maxmin.ipynb", "notebooks/02/bim-rawmaterialplanning.ipynb", "notebooks/02/lad-regression.ipynb", "notebooks/02/mad-portfolio-optimization.ipynb", "notebooks/02/multiproductionfaciliity_worstcase.ipynb", "notebooks/03/03.00.md", "notebooks/03/bim-perturbed.ipynb", "notebooks/03/bim-production-revisited.ipynb", "notebooks/03/cryptarithms.ipynb", "notebooks/03/facility-location.ipynb", "notebooks/03/job-shop-scheduling.ipynb", "notebooks/03/machine-scheduling.ipynb", "notebooks/03/maintenance-planning.ipynb", "notebooks/03/recharging-electric-vehicle.ipynb", "notebooks/03/shift-scheduling.ipynb", "notebooks/03/simple-production-model-gdp.ipynb", "notebooks/03/strip-packing.ipynb", "notebooks/04/04.00.md", "notebooks/04/cryptocurrency-arbitrage.ipynb", "notebooks/04/dinner-seat-allocation.ipynb", "notebooks/04/forex-arbitrage.ipynb", "notebooks/04/gasoline-distribution.ipynb", "notebooks/04/graph-coloring.ipynb", "notebooks/04/mincost-flow.ipynb", "notebooks/04/power-network.ipynb", "notebooks/05/05.00.md", "notebooks/05/cutting-stock.ipynb", "notebooks/05/markowitz_portfolio.ipynb", "notebooks/05/milk-pooling.ipynb", "notebooks/05/ols-regression.ipynb", "notebooks/05/refinery-production.ipynb", "notebooks/05/svm.ipynb", "notebooks/06/06.00.md", "notebooks/06/building-insulation.ipynb", "notebooks/06/economic-order-quantity.ipynb", "notebooks/06/investment-wheel.ipynb", "notebooks/06/kelly-criterion.ipynb", "notebooks/06/markowitz_portfolio_revisited.ipynb", "notebooks/06/optimal-growth-portfolios.ipynb", "notebooks/06/svm-conic.ipynb", "notebooks/07/07.00.md", "notebooks/07/bim-robustness-analysis.ipynb", "notebooks/07/fleet-assignment.ipynb", "notebooks/08/08.00.md", "notebooks/08/bim-robust-optimization.ipynb", "notebooks/09/09.00.md", "notebooks/09/economicdispatch.ipynb", "notebooks/09/markowitz_portfolio_with_chance_constraint.ipynb", "notebooks/09/pop-up_shop.ipynb", "notebooks/09/seafood.ipynb", "notebooks/10/10.00.md", "notebooks/10/airline-seating.ipynb", "notebooks/10/ccg.ipynb", "notebooks/10/farmer.ipynb", "notebooks/10/opf-ldr.ipynb", "notebooks/10/opf-wind-curtailment.ipynb", "notebooks/appendix/appendix.md", "notebooks/appendix/functional-programming-pyomo.ipynb", "notebooks/appendix/pyomo-style-guide.md"], "titles": ["Index", "Hands-On Optimization with Python", "1. Mathematical Optimization", "A first production planning problem", "A data-driven Pyomo Model", "A basic Pyomo model", "2. Linear Optimization", "Extra material: Wine quality prediction with \\(L_1\\) regression", "BIM production", "Dual of the BIM production problem", "BIM production variants", "BIM production for worst case", "BIM production using demand forecasts", "Least Absolute Deviation (LAD) Regression", "Mean Absolute Deviation (MAD) portfolio optimization", "Extra material: Multi-product facility production", "3. Mixed Integer Linear Optimization", "BIM production with perturbed data", "BIM production revisited", "Extra material: Cryptarithms puzzle", "Facility location problem", "Extra material: Job shop scheduling", "Machine Scheduling", "Extra material: Maintenance planning", "Recharging strategy for an electric vehicle", "Workforce shift scheduling", "Production model using disjunctions", "Extra material: Strip packing", "4. Network Optimization", "Cryptocurrency arbitrage search", "Dinner seating arrangement", "Extra material: Forex Arbitrage", "Gasoline distribution", "Exam room scheduling", "Minimum-Cost Flow Problem", "Extra material: Energy dispatch problem", "5. Convex Optimization", "Extra Material: Cutting Stock", "Markowitz portfolio optimization", "Milk pooling and blending", "Ordinary Least Squares (OLS) Regression", "Extra material: Refinery production and shadow pricing with CVXPY", "Support Vector Machines for Binary Classification", "6. Conic Optimization", "Optimal Design of Multilayered Building Insulation", "Economic Order Quantity", "Extra material: Luenberger\u2019s Investment Wheel", "The Kelly Criterion", "Markowitz portfolio optimization revisited", "Extra material: Optimal Growth Portfolios with Risk Aversion", "Training Support Vector Machines with Conic Optimization", "7. Accounting for Uncertainty: Optimization Meets Reality", "Robustness analysis of BIM production plan via simulations", "Fleet assignment problem", "8. Robust Optimization - Single Stage Problems", "Robust BIM microchip production problem", "9. Stochastic Optimization - Single Stage Problems", "Economic dispatch in energy systems", "Markowitz portfolio optimization with chance constraints", "Pop-up shop", "Stock optimization for seafood distribution center", "10. Two-Stage Problems", "Airline seat allocation problem", "Two-stage Production Planning", "Extra: The farmer\u2019s problem and its variants", "Optimal power flow problem with recourse actions", "Extra: Two-stage energy dispatch optimization with wind curtailment", "Appendix: Working with Pyomo", "Functional Programming with Pyomo", "Pyomo style guide"], "terms": {"welcom": [1, 5, 69], "thi": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69], "repositori": [1, 7, 25, 57], "companion": [1, 5, 6, 16, 28, 36, 43, 54, 56, 61], "notebook": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 55, 57, 60, 63, 65, 66, 67, 68], "book": [1, 8, 15, 20, 22, 35, 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27, 29, 33, 35, 37, 42, 44, 45, 48, 50, 53, 55, 60, 62, 63, 65, 66, 69], "action": [2, 61, 66], "choic": [2, 4, 15, 21, 24, 26, 35, 37, 39, 42, 44, 57, 68, 69], "whether": [2, 8, 22, 24, 26, 27, 29, 31, 33, 35, 36, 44, 45, 53, 57, 63, 66], "new": [2, 4, 5, 7, 8, 13, 17, 21, 23, 25, 26, 27, 29, 30, 32, 35, 37, 39, 41, 42, 45, 48, 55, 59, 62, 63, 66, 68, 69], "manufactur": [2, 8, 17, 27, 34, 41, 63], "facil": [2, 6, 16, 21, 26, 27, 34, 39, 45], "suppli": [2, 4, 30, 32, 34, 35, 39, 57, 66], "rout": [2, 29, 51, 53, 62], "price": [2, 3, 4, 10, 11, 12, 18, 29, 31, 32, 37, 39, 49, 52, 59, 60, 62, 63, 64, 68, 69], "should": [2, 3, 8, 14, 15, 18, 22, 23, 24, 25, 26, 29, 33, 34, 36, 37, 39, 42, 47, 50, 53, 55, 57, 59, 63, 64, 65, 66, 68, 69], "sell": [2, 3, 11, 15, 18, 26, 29, 31, 32, 38, 39, 59, 60, 62, 63, 64], "product": [2, 5, 6, 16, 20, 23, 34, 35, 36, 37, 39, 42, 45, 46, 50, 51, 54, 57, 61, 64, 65, 66], "function": [2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 18, 19, 20, 21, 22, 25, 26, 27, 29, 30, 32, 33, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 67, 69], "evalu": [2, 5, 13, 42, 50, 63], "specif": [2, 3, 5, 6, 8, 10, 13, 14, 15, 17, 20, 25, 29, 30, 34, 35, 37, 39, 41, 42, 45, 48, 53, 55, 57, 59, 60, 62, 63, 65, 67, 68, 69], "i": [2, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 66, 69], "e": [2, 5, 7, 18, 19, 21, 22, 25, 27, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 53, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "valu": [2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 66, 68, 69], "earlier": [2, 5, 10, 21, 42, 45, 48, 52, 57, 59], "For": [2, 3, 5, 8, 10, 14, 16, 18, 20, 21, 22, 24, 27, 29, 30, 31, 34, 35, 36, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "specifi": [2, 4, 5, 8, 13, 21, 24, 27, 29, 30, 31, 34, 37, 38, 39, 42, 45, 46, 48, 50, 58, 66, 68, 69], "either": [2, 3, 4, 5, 20, 21, 22, 23, 24, 26, 27, 29, 35, 50, 59, 63, 65, 69], "maxim": [2, 3, 4, 5, 6, 8, 9, 10, 17, 18, 20, 23, 26, 29, 30, 31, 35, 37, 38, 39, 41, 46, 47, 48, 49, 55, 58, 60, 62, 63, 64, 68, 69], "minim": [2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 18, 20, 21, 22, 24, 25, 27, 29, 33, 34, 35, 37, 40, 42, 44, 45, 50, 52, 53, 55, 57, 64, 65, 66, 69], "In": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69], "oper": [2, 3, 15, 21, 22, 27, 29, 35, 37, 39, 41, 42, 44, 45, 53, 59, 62, 63, 65, 66, 68], "cost": [2, 3, 4, 5, 6, 11, 12, 14, 15, 18, 20, 26, 28, 29, 30, 31, 33, 35, 37, 39, 41, 44, 45, 52, 53, 57, 59, 60, 63, 64, 65, 66, 68], "number": [2, 3, 4, 5, 8, 9, 10, 13, 16, 17, 18, 19, 20, 22, 24, 25, 27, 29, 31, 33, 35, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69], "satisfi": [2, 3, 9, 15, 16, 18, 19, 20, 27, 29, 30, 31, 32, 34, 39, 42, 46, 47, 49, 57, 59, 62, 65], "custom": [2, 20, 21, 29, 32, 37, 39, 42, 51, 57, 62, 69], "restrict": [2, 16, 25, 30, 33, 35, 46, 49, 53, 55, 68, 69], "possibl": [2, 4, 5, 6, 9, 13, 15, 16, 17, 18, 19, 20, 21, 24, 27, 29, 30, 32, 33, 34, 35, 38, 39, 40, 42, 47, 50, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69], "condit": [2, 3, 8, 15, 18, 23, 24, 26, 27, 29, 30, 39, 42, 44, 50, 55, 59, 64, 68, 69], "must": [2, 3, 5, 19, 21, 23, 26, 27, 29, 31, 32, 35, 38, 39, 44, 53, 63, 64, 65, 66, 68], "requir": [2, 3, 4, 8, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 37, 39, 45, 47, 52, 53, 57, 59, 62, 63, 64, 66, 68, 69], "maximum": [2, 3, 8, 11, 15, 18, 23, 24, 25, 29, 33, 34, 35, 39, 44, 47, 48, 49, 53, 55, 57, 63, 66, 68], "allow": [2, 4, 8, 18, 23, 24, 27, 29, 31, 32, 35, 41, 45, 48, 49, 53, 55, 57, 65, 68], "budget": [2, 12, 37, 52, 63], "demand": [2, 3, 4, 6, 18, 20, 26, 30, 32, 34, 35, 37, 39, 45, 51, 52, 57, 59, 63, 64, 65, 66, 68, 69], "import": [2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 58, 59, 60, 63, 64, 69], "met": [2, 35, 39, 57], "capac": [2, 12, 18, 23, 24, 30, 34, 35, 41, 52, 57, 62, 66, 69], "warehous": [2, 18, 45, 51, 60, 69], "exceed": [2, 29, 30, 39, 57], "both": [2, 4, 5, 8, 12, 13, 17, 20, 23, 24, 26, 27, 29, 33, 35, 37, 38, 39, 42, 45, 47, 50, 61, 62, 63], "express": [2, 3, 4, 7, 8, 9, 10, 11, 12, 16, 18, 19, 22, 26, 29, 30, 32, 34, 35, 39, 41, 42, 44, 45, 46, 49, 50, 52, 55, 57, 60, 64, 65, 66, 68, 69], "defin": [2, 4, 5, 8, 9, 12, 13, 14, 16, 20, 22, 25, 26, 27, 32, 33, 35, 37, 39, 40, 41, 42, 45, 46, 50, 53, 55, 57, 62, 63, 65, 66, 68, 69], "feasibl": [2, 5, 8, 9, 17, 20, 30, 35, 37, 41, 44, 46, 47, 49, 53, 60, 63, 65, 66], "region": [2, 8, 20, 32, 35], "set": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 44, 45, 46, 47, 48, 49, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "candid": [2, 3, 7, 21, 37], "meet": [2, 3, 5, 12, 18, 22, 25, 29, 30, 32, 35, 37, 39, 43, 52, 57, 59, 65, 66], "best": [2, 5, 7, 8, 29, 30, 35, 44, 57, 63, 66, 69], "global": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 44, 46, 48, 52, 55, 57, 60, 62, 66, 69], "optimum": [2, 39, 41, 44], "among": [2, 3, 7, 11, 14, 15, 21, 22, 26, 31, 32, 33, 47, 48, 49, 62, 64, 65, 69], "appli": [2, 4, 5, 18, 24, 35, 37, 39, 42, 44, 45, 49, 65, 66, 68], "type": [2, 3, 4, 5, 6, 8, 12, 16, 17, 19, 21, 25, 29, 30, 35, 37, 42, 45, 50, 52, 55, 57, 65, 66, 68], "relat": [2, 5, 18, 23, 26, 29, 33, 50, 55, 57, 62, 63, 65], "fundament": [2, 14, 39, 68], "question": [2, 8, 15, 22, 29, 42, 45, 51, 59, 64, 65], "translat": [2, 4, 5, 18, 22, 29, 32, 37, 44], "real": [2, 4, 5, 7, 13, 16, 21, 30, 31, 35, 36, 37, 40, 46, 47, 49, 51, 53, 55, 57, 59, 62, 63, 65], "abstract": [2, 4, 8, 68], "represent": [2, 21, 42, 44, 50], "Not": [2, 29], "aspect": [2, 6, 8, 14, 16, 28, 36, 43, 54, 56, 61], "taken": [2, 29, 33, 63, 65, 69], "account": [2, 10, 18, 23, 24, 29, 31, 35, 43, 46, 47, 55, 59, 60, 63, 65, 66, 68], "so": [2, 3, 4, 5, 8, 9, 13, 18, 21, 23, 24, 25, 27, 29, 30, 35, 36, 37, 38, 39, 40, 42, 44, 48, 50, 51, 53, 55, 57, 62, 63, 66, 68], "mani": [2, 3, 4, 8, 16, 19, 20, 22, 23, 27, 29, 30, 31, 33, 37, 42, 45, 46, 47, 49, 50, 52, 53, 55, 59, 62, 63, 65, 66, 69], "made": [2, 3, 10, 12, 18, 20, 24, 29, 52, 59, 63, 66], "step": [2, 3, 4, 8, 9, 12, 14, 15, 18, 21, 29, 45, 46, 52, 53, 62, 63, 68, 69], "typic": [2, 21, 35, 57, 59, 63, 68, 69], "signific": [2, 5, 8, 41, 45, 46, 47, 49, 50], "impact": [2, 7, 39, 51, 64], "approach": [2, 5, 7, 8, 10, 13, 14, 17, 19, 20, 22, 26, 27, 30, 33, 37, 39, 44, 46, 49, 57, 63, 65, 68], "There": [2, 5, 18, 19, 22, 25, 26, 29, 30, 35, 37, 39, 44, 45, 59, 63, 68, 69], "multipl": [2, 3, 12, 15, 18, 27, 29, 31, 32, 34, 37, 39, 69], "equival": [2, 5, 8, 18, 20, 22, 33, 42, 44, 45, 53, 55, 58, 62, 69], "formul": [2, 3, 4, 6, 8, 9, 11, 13, 14, 15, 16, 18, 22, 23, 26, 27, 28, 29, 30, 32, 35, 36, 39, 40, 44, 49, 51, 55, 57, 59, 60, 62, 65, 66, 69], "conceptu": 2, "same": [2, 3, 4, 5, 10, 11, 13, 14, 15, 18, 19, 21, 22, 25, 27, 29, 30, 31, 32, 33, 34, 40, 42, 45, 46, 50, 53, 55, 57, 60, 63, 65, 66, 68, 69], "comput": [2, 4, 5, 7, 8, 14, 15, 18, 22, 23, 29, 30, 31, 35, 37, 39, 42, 45, 46, 49, 50, 52, 59, 62, 64, 65, 66, 68, 69], "complex": [2, 4, 5, 15, 21, 22, 23, 29, 31, 37, 68, 69], "mai": [2, 3, 4, 5, 10, 11, 12, 15, 16, 17, 18, 20, 21, 23, 27, 29, 31, 32, 35, 37, 39, 41, 42, 45, 46, 50, 52, 55, 57, 58, 64, 68], "differ": [2, 3, 5, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 27, 29, 30, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 45, 48, 49, 50, 51, 53, 55, 57, 59, 60, 63, 64, 65, 66, 69], "interpret": [2, 4, 15, 33, 41], "s": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "after": [2, 5, 13, 23, 29, 30, 31, 40, 47, 53, 55, 59, 63, 64, 65, 66, 68], "ha": [2, 3, 4, 5, 7, 10, 12, 14, 18, 21, 22, 24, 25, 26, 27, 29, 30, 31, 33, 35, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68], "back": [2, 5, 13, 23, 29, 31, 33, 42, 50, 63, 68], "origin": [2, 3, 4, 8, 9, 10, 13, 14, 17, 25, 27, 30, 35, 37, 39, 45, 48], "These": [2, 4, 15, 25, 27, 29, 34, 35, 39, 42, 45, 47, 49, 53, 57, 59, 62, 68, 69], "treat": [2, 21, 30, 39, 51, 66], "continu": [2, 12, 18, 22, 23, 39, 42, 44, 50, 52, 60, 66], "process": [2, 4, 23, 29, 39, 41, 42, 45, 50, 53, 55, 68, 69], "sequenti": 2, "final": [2, 4, 5, 12, 14, 21, 22, 23, 29, 31, 39, 45, 62, 65], "turn": [2, 3, 16, 21, 30, 36, 42, 50, 53, 57, 66], "out": [2, 3, 23, 24, 27, 29, 30, 32, 36, 37, 53, 57, 65, 66], "impract": [2, 29], "adjust": [2, 4, 14, 29, 35, 41, 57, 62, 65, 66], "certain": [2, 16, 29, 30, 32, 42, 45, 50, 55, 57, 62, 66], "desir": [2, 3, 12, 18, 25, 30, 36, 52, 68], "properti": [2, 8, 30, 36, 44, 46, 48, 49, 57], "cannot": [2, 8, 12, 16, 21, 22, 25, 29, 33, 35, 44, 52, 53, 60, 62, 63, 66], "effici": [2, 10, 14, 21, 27, 29, 30, 48, 49, 50, 55, 69], "perhap": [2, 19, 32, 37], "re": [2, 69], "includ": [2, 5, 6, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 29, 31, 32, 36, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 53, 55, 57, 58, 62, 63, 64, 65, 66, 67, 68, 69], "well": [2, 5, 7, 13, 14, 19, 22, 27, 36, 37, 44, 46, 47, 60, 64, 69], "except": [2, 20, 25, 33, 66, 68, 69], "mathematician": 2, "studi": [2, 15, 21, 27, 29, 37, 39, 44, 57, 60, 69], "alwai": [2, 4, 10, 12, 17, 24, 35, 38, 40, 42, 46, 47, 48, 50, 51, 55, 58, 62, 68], "flaw": 2, "challeng": [2, 8, 19, 27, 31, 37, 39, 42], "follow": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "given": [2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 35, 37, 39, 42, 44, 45, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "f": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "x": [2, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 59, 60, 63, 64, 65, 66, 68, 69], "mathbb": [2, 6, 8, 13, 16, 17, 18, 26, 35, 37, 38, 40, 42, 45, 46, 47, 49, 50, 55, 57, 58, 59, 60, 62, 65, 66], "r": [2, 4, 6, 8, 13, 14, 16, 18, 19, 21, 22, 24, 25, 27, 29, 31, 32, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 58, 59, 60, 62, 63, 64, 65, 66, 68], "subseteq": [2, 16, 33, 35, 53], "n": [2, 6, 7, 8, 9, 13, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 69], "being": [2, 5, 6, 8, 33, 35, 38, 39, 50, 53, 66], "y": [2, 4, 7, 8, 9, 13, 14, 18, 19, 20, 23, 24, 26, 27, 29, 30, 31, 32, 34, 35, 38, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 55, 57, 59, 60, 63, 64, 66, 68, 69], "geq": [2, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 55, 57, 58, 60, 62, 63, 65, 66, 68], "foral": [2, 4, 7, 11, 12, 13, 14, 15, 18, 19, 20, 22, 23, 24, 25, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 45, 46, 48, 49, 50, 53, 55, 57, 59, 62, 63, 65, 66], "least": [2, 6, 7, 12, 18, 22, 24, 33, 35, 36, 37, 39, 52, 53, 63, 64], "good": [2, 4, 5, 7, 15, 20, 27, 29, 33, 34, 38, 46, 49, 59, 63, 64, 69], "similarli": [2, 8, 13, 18, 35, 40], "chang": [2, 4, 5, 10, 14, 15, 21, 23, 24, 27, 29, 30, 31, 32, 33, 35, 38, 39, 40, 41, 48, 51, 53, 55, 57, 58, 62, 63, 65, 68, 69], "last": [2, 12, 18, 22, 23, 24, 38, 39, 52, 53, 55, 64, 66], "leq": [2, 3, 4, 8, 9, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 62, 63, 65, 66, 69], "case": [2, 3, 4, 5, 7, 8, 13, 16, 20, 21, 25, 26, 27, 29, 30, 32, 37, 38, 39, 40, 42, 46, 47, 49, 50, 55, 57, 59, 60, 66, 68, 69], "refer": [2, 3, 4, 6, 8, 13, 16, 20, 24, 27, 29, 32, 34, 39, 40, 42, 47, 50, 65, 69], "begin": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "align": [2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "min": [2, 6, 7, 8, 9, 11, 13, 14, 16, 18, 20, 22, 24, 25, 27, 29, 30, 32, 33, 34, 35, 37, 39, 40, 42, 44, 45, 46, 50, 53, 55, 57, 59, 60, 63, 65, 66, 69], "quad": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 58, 59, 60, 62, 63, 65, 68, 69], "text": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "t": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "end": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "lead": [2, 14, 17, 18, 19, 20, 21, 22, 26, 29, 36, 39, 42, 44, 50, 55, 57, 63, 66, 69], "techniqu": [2, 7, 11, 13, 21, 22, 23, 26, 32, 42, 45, 49, 57, 63, 65], "introductori": [2, 61], "present": [2, 4, 5, 7, 8, 13, 14, 24, 29, 31, 32, 35, 37, 39, 40, 41, 42, 46, 47, 48, 49, 50, 53, 62, 64, 66, 68, 69], "simpl": [2, 3, 4, 5, 12, 21, 26, 30, 31, 36, 37, 39, 41, 42, 45, 50, 55, 68, 69], "context": [2, 15, 25, 33, 34, 58, 63, 66], "plan": [2, 4, 5, 10, 11, 15, 16, 18, 24, 25, 27, 45, 51, 59, 61], "explain": [2, 7, 35, 39, 50, 57, 66], "structur": [2, 4, 8, 17, 26, 28, 29, 30, 37, 44, 62, 63, 65, 66, 68, 69], "formal": [2, 16], "implement": [2, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 22, 24, 27, 28, 29, 32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 51, 54, 56, 57, 58, 59, 61, 62, 63, 68, 69], "second": [2, 4, 5, 10, 13, 18, 21, 27, 29, 31, 32, 33, 35, 37, 38, 39, 42, 50, 60, 61, 62, 63, 64, 65, 66], "also": [2, 3, 4, 5, 8, 11, 12, 14, 15, 18, 20, 22, 23, 25, 29, 30, 35, 36, 38, 39, 41, 42, 45, 53, 55, 58, 62, 63, 65, 66, 69], "serv": [2, 4, 5, 20, 34, 53, 63], "tutori": [2, 25, 37, 46, 47, 69], "lastli": [2, 3, 62, 63, 66], "discuss": [2, 32, 42, 45, 50, 51, 63], "some": [2, 3, 4, 5, 7, 8, 13, 16, 21, 23, 27, 29, 30, 32, 33, 35, 39, 40, 41, 42, 44, 46, 47, 49, 50, 55, 57, 63, 65, 66, 68, 69], "advanc": [2, 3, 5, 23, 39, 45, 51, 63, 65, 66], "featur": [2, 4, 5, 6, 8, 13, 16, 20, 21, 22, 23, 27, 34, 39, 40, 47, 49, 60, 62, 68, 69], "third": [2, 4, 5, 32], "go": [2, 6, 8, 13, 14, 16, 21, 28, 30, 35, 36, 39, 40, 43, 51, 53, 54, 56, 63, 64, 65, 68], "next": [2, 3, 4, 5, 6, 7, 8, 12, 15, 16, 18, 21, 22, 23, 25, 28, 29, 30, 32, 34, 36, 38, 43, 46, 50, 51, 53, 54, 56, 57, 60, 64, 65, 66], "about": [2, 6, 8, 16, 20, 24, 28, 29, 30, 36, 43, 51, 54, 56, 57, 59, 62, 63, 65], "linear": [2, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 22, 23, 26, 29, 31, 35, 36, 39, 40, 41, 55, 57, 60, 61, 62, 63, 65], "compani": [3, 6, 8, 12, 17, 18, 34, 39, 45, 51, 52, 53, 55, 63], "produc": [3, 4, 7, 8, 10, 12, 15, 17, 21, 23, 26, 29, 31, 32, 35, 37, 39, 42, 46, 47, 52, 53, 55, 57, 63, 65, 66, 68], "two": [3, 4, 5, 6, 8, 12, 13, 14, 16, 17, 19, 20, 21, 23, 25, 26, 29, 30, 31, 32, 33, 37, 39, 42, 45, 47, 50, 53, 55, 56, 57, 59, 60, 65, 68, 69], "version": [3, 4, 5, 10, 18, 20, 30, 35, 39, 45, 53, 54, 55, 63, 65, 66, 69], "each": [3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 42, 46, 47, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "raw": [3, 5, 8, 12, 18, 26, 29, 35, 39, 42, 50, 52, 57, 63, 65, 66], "10": [3, 4, 5, 7, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "per": [3, 8, 10, 12, 14, 18, 23, 24, 25, 26, 29, 32, 34, 37, 44, 45, 52, 60, 63, 64, 65], "gram": [3, 18, 42, 50], "special": [3, 4, 11, 12, 13, 16, 28, 30, 37, 40, 45, 62, 69], "labor": [3, 4, 26, 63, 68], "finish": [3, 12, 18, 21, 22, 23, 26, 37, 52, 53, 69], "u": [3, 4, 5, 14, 18, 23, 29, 34, 42, 44, 45, 46, 49, 50, 53, 55, 57, 63, 68, 69], "higher": [3, 14, 26, 29, 39, 42, 47, 50, 52, 57, 59, 63, 65], "270": [3, 4, 5, 26, 29, 63, 66, 68], "unit": [3, 4, 5, 10, 12, 14, 15, 18, 23, 24, 26, 29, 31, 32, 34, 35, 39, 44, 45, 47, 52, 57, 58, 59, 60, 62, 63, 64, 65, 68], "one": [3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 18, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 62, 63, 64, 65, 66], "hour": [3, 4, 21, 24, 25, 26, 53, 63], "b": [3, 4, 5, 6, 7, 8, 13, 15, 16, 18, 19, 21, 22, 25, 26, 29, 32, 34, 35, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 53, 60, 62, 63, 65, 66, 68, 69], "due": [3, 4, 12, 14, 18, 29, 35, 38, 39, 51, 52, 55, 59, 62, 64, 65, 69], "market": [3, 4, 14, 15, 29, 31, 39, 46, 47, 49, 62, 63, 64], "limit": [3, 5, 12, 18, 20, 21, 24, 25, 26, 29, 32, 35, 37, 39, 41, 44, 46, 49, 52, 57, 63, 65, 66, 69], "40": [3, 4, 5, 7, 24, 25, 26, 29, 32, 33, 37, 44, 45, 46, 59, 62, 63, 64, 68, 69], "week": [3, 25, 29, 33, 62], "v": [3, 4, 5, 14, 20, 21, 24, 29, 30, 33, 34, 35, 39, 42, 45, 46, 50, 53, 57, 63, 65, 66, 68, 69], "lower": [3, 4, 5, 12, 14, 21, 29, 31, 32, 37, 39, 40, 55, 59, 62, 64, 65, 69], "unlimit": [3, 4, 26, 37, 63], "210": [3, 4, 5, 26, 62, 63, 64, 68], "9": [3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 41, 42, 45, 50, 51, 52, 53, 55, 62, 63, 66, 68], "1": [3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 37, 38, 40, 41, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 66, 68, 69], "summar": [3, 4, 25, 32, 35, 39, 42, 50, 59, 62, 63, 64], "tabl": [3, 4, 18, 21, 22, 24, 26, 27, 31, 42, 46, 52, 53, 55, 59, 60, 62, 64, 69], "g": [3, 4, 5, 8, 14, 18, 20, 22, 27, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 44, 45, 50, 53, 55, 60, 65, 66, 68], "hr": [3, 4, 24, 53], "2": [3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 37, 38, 40, 41, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 63, 65, 66, 68, 69], "weekli": [3, 25], "avail": [3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 66, 68], "inventori": [3, 12, 18, 29, 45, 52, 59, 60], "shelf": 3, "life": [3, 22, 30, 36, 44, 53], "order": [3, 4, 10, 12, 18, 21, 22, 25, 30, 32, 35, 37, 41, 42, 43, 50, 52, 53, 59, 63], "left": [3, 7, 8, 9, 10, 12, 13, 21, 22, 23, 24, 25, 27, 30, 32, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 57, 60, 62, 63, 65], "over": [3, 4, 10, 11, 14, 18, 21, 23, 25, 29, 30, 35, 37, 39, 41, 42, 45, 47, 50, 52, 59, 62, 63, 64, 68, 69], "discard": 3, "detail": [3, 8, 20, 25, 42, 44, 50, 59], "resourc": [3, 4, 15, 21, 25, 27, 29, 30, 37, 52, 64, 65, 68], "amount": [3, 4, 12, 15, 16, 17, 18, 21, 22, 25, 29, 31, 32, 34, 38, 39, 51, 52, 55, 57, 58, 60, 63, 64, 65, 69], "80": [3, 4, 5, 26, 29, 32, 35, 41, 47, 49, 50, 63, 64, 66, 68], "50": [3, 4, 5, 9, 14, 18, 24, 26, 29, 31, 32, 35, 37, 39, 42, 44, 45, 52, 55, 60, 62, 63, 64, 66, 68, 69], "100": [3, 4, 5, 10, 18, 19, 20, 22, 24, 26, 29, 31, 32, 35, 37, 38, 39, 41, 42, 45, 47, 49, 50, 52, 55, 57, 60, 62, 63, 64, 65, 66, 68, 69], "want": [3, 14, 17, 18, 20, 29, 32, 33, 38, 40, 42, 48, 55, 58, 62, 63, 69], "its": [3, 5, 7, 8, 9, 13, 14, 20, 22, 30, 34, 37, 40, 42, 45, 50, 55, 63, 65, 68, 69], "gross": [3, 46, 47, 49], "profit": [3, 4, 5, 6, 8, 9, 10, 17, 23, 26, 29, 32, 37, 39, 41, 55, 62, 63, 64, 68, 69], "much": [3, 8, 12, 13, 17, 18, 23, 24, 27, 30, 33, 37, 44, 47, 51, 63, 65, 66], "abov": [3, 4, 6, 8, 11, 12, 13, 14, 17, 18, 22, 23, 24, 29, 30, 32, 33, 35, 37, 40, 44, 45, 46, 48, 49, 50, 52, 55, 57, 60, 62, 63, 65, 69], "optim": [3, 4, 5, 9, 10, 11, 13, 17, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 41, 45, 46, 52, 53, 55, 57, 59, 61, 67, 69], "reformul": [3, 5, 10, 13, 14, 44, 46, 47, 49, 50, 55, 62], "involv": [3, 5, 6, 8, 11, 21, 31, 39, 42, 45, 46, 47, 49], "few": [3, 4, 5, 29, 32, 33, 42, 62, 68], "crucial": [3, 35], "element": [3, 4, 5, 8, 25, 30, 32, 42, 44, 47, 50, 65, 68, 69], "start": [3, 5, 7, 8, 13, 14, 18, 21, 22, 23, 24, 27, 29, 31, 33, 37, 49, 55, 62, 63], "point": [3, 4, 7, 8, 13, 16, 20, 23, 27, 29, 34, 39, 40, 41, 42, 45, 47, 50, 55, 60, 62, 66, 69], "list": [3, 4, 8, 14, 19, 21, 24, 25, 26, 29, 30, 31, 33, 35, 37, 42, 44, 46, 49, 50, 52, 53, 57, 60, 62, 63, 65, 68, 69], "relev": [3, 4, 18, 20, 27, 29, 66, 68, 69], "hand": [3, 4, 8, 9, 17, 20, 24, 25, 29, 30, 31, 42, 50, 55, 57, 59], "quantiti": [3, 8, 11, 12, 18, 34, 35, 37, 39, 43, 51, 52, 55, 63], "modifi": [3, 5, 17, 20, 21, 23, 29, 31, 42, 55, 57, 62, 65, 66, 68, 69], "achiev": [3, 11, 14, 23, 25, 38, 42, 50, 65, 68], "outcom": [3, 15, 32, 42, 46, 50, 57, 59, 63], "while": [3, 5, 8, 9, 12, 14, 17, 18, 20, 21, 24, 25, 26, 29, 33, 34, 35, 37, 42, 48, 49, 50, 51, 52, 53, 55, 57, 59, 62, 63, 65, 66], "stage": [3, 5, 27, 39, 46, 47, 60, 64, 65, 68, 69], "prove": [3, 8], "redund": [3, 69], "later": [3, 4, 5, 15, 21, 24, 27, 45, 47, 66, 69], "creat": [3, 12, 13, 14, 15, 19, 21, 22, 23, 27, 29, 30, 31, 33, 37, 39, 42, 45, 46, 49, 50, 57, 59, 62, 63, 64, 68, 69], "comprehens": [3, 7, 42, 50], "below": [3, 5, 9, 11, 12, 14, 17, 20, 21, 24, 29, 30, 35, 37, 39, 42, 44, 45, 46, 50, 55, 57, 60, 62, 63, 66, 69], "symbol": [3, 14, 22, 29, 31, 32, 49, 59, 68, 69], "descript": [3, 15, 21, 32, 42, 51, 55, 66], "upper": [3, 4, 5, 9, 12, 14, 21, 22, 23, 24, 29, 32, 33, 37, 38, 39, 40, 44, 45, 52, 55, 60, 68, 69], "bound": [3, 4, 5, 9, 14, 19, 21, 22, 23, 24, 26, 29, 30, 31, 33, 37, 38, 39, 42, 44, 53, 55, 57, 63, 64, 66, 68], "known": [3, 4, 5, 7, 13, 14, 19, 21, 22, 23, 27, 33, 38, 39, 40, 42, 44, 45, 47, 49, 50, 53, 57, 59, 63, 64, 65, 66], "x_m": [3, 5, 60], "0": [3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "x_a": [3, 5], "x_b": [3, 5], "y_u": [3, 5], "y_v": [3, 5], "measur": [3, 7, 10, 14, 23, 24, 25, 29, 39, 42, 50, 51], "max": [3, 4, 7, 8, 9, 10, 11, 14, 15, 17, 21, 22, 23, 24, 25, 26, 27, 29, 35, 37, 38, 39, 41, 42, 44, 46, 47, 48, 50, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "equal": [3, 5, 6, 7, 8, 10, 12, 15, 16, 23, 25, 26, 27, 29, 30, 32, 33, 34, 38, 39, 40, 41, 44, 45, 46, 47, 49, 53, 55, 57, 59, 60, 62, 63, 65, 66], "between": [3, 4, 5, 8, 10, 13, 14, 20, 21, 24, 25, 27, 29, 31, 32, 34, 35, 36, 38, 39, 40, 42, 44, 46, 47, 48, 50, 53, 57, 64, 65, 66, 68, 69], "revenu": [3, 4, 5, 10, 11, 41, 59, 62, 64, 68], "written": [3, 4, 5, 15, 42, 45, 58, 59, 62, 68, 69], "As": [3, 4, 5, 8, 14, 18, 21, 25, 29, 30, 31, 39, 42, 45, 46, 50, 53, 59, 60, 63, 66, 69], "shown": [3, 5, 39, 42, 45, 46, 69], "here": [3, 4, 5, 10, 12, 13, 21, 22, 24, 25, 26, 29, 31, 39, 40, 42, 45, 46, 47, 49, 52, 53, 55, 57, 58, 59, 62, 63, 66, 68, 69], "algebra": [3, 5, 19, 41, 42, 45], "combin": [3, 4, 5, 18, 19, 29, 39, 44, 53, 57, 63, 65, 68, 69], "name": [3, 4, 5, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 29, 30, 32, 37, 40, 41, 42, 48, 50, 59, 60, 62, 65, 66], "when": [3, 4, 5, 7, 8, 12, 13, 16, 20, 21, 22, 23, 24, 25, 29, 31, 32, 35, 38, 39, 41, 42, 43, 45, 46, 47, 50, 57, 59, 60, 63, 64, 65, 66, 67, 68], "place": [3, 4, 29, 30, 31, 35, 39, 45, 46, 59, 68, 69], "break": [3, 4, 29, 33, 53, 57, 63, 66], "up": [3, 4, 5, 12, 16, 17, 18, 19, 21, 23, 29, 37, 39, 42, 46, 47, 50, 52, 56, 57, 62, 63, 64], "longer": [3, 20, 21, 30, 45, 50, 53, 57, 62, 68], "smaller": [3, 4, 10, 16, 27, 51, 57], "simplifi": [3, 5, 24, 27, 50, 62, 68, 69], "relationship": [3, 5, 13, 22, 24, 25, 27, 29, 31, 44, 45, 46, 69], "inequ": [3, 6, 8, 9, 39, 47, 55, 65], "overal": [3, 8, 15, 25, 39, 44], "now": [3, 4, 5, 7, 8, 12, 14, 18, 20, 21, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 42, 45, 46, 47, 48, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "readi": [3, 29, 31, 45, 50, 63], "full": [3, 7, 13, 20, 23, 24, 32, 37, 39, 40, 42, 44, 49, 50, 55, 62, 63, 69], "canon": [3, 6, 38], "nonumb": [3, 4, 30], "textbook": [3, 20, 63, 64], "customari": [3, 8, 50], "under": [3, 14, 15, 18, 20, 25, 26, 31, 42, 52, 57, 59, 62, 63, 64, 68], "clearli": [3, 4, 7, 18, 20, 23, 25, 39, 53, 63, 66], "distinguish": [3, 29, 66, 69], "paramet": [3, 4, 5, 18, 21, 23, 32, 33, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 55, 57, 59, 60, 62, 63, 65, 66, 68], "might": [3, 15, 16, 27, 29, 31, 33, 35, 36, 39, 42, 51, 59, 65, 68], "letter": [3, 19, 45, 63], "throughout": [3, 8, 29, 63, 69], "websit": 3, "howev": [3, 4, 8, 13, 15, 16, 17, 18, 20, 28, 29, 30, 31, 33, 35, 36, 39, 42, 44, 45, 48, 49, 50, 53, 55, 57, 59, 62, 63, 65, 66, 69], "stick": 3, "convent": [3, 5, 6, 8, 57, 65, 66], "onli": [3, 4, 7, 8, 9, 16, 18, 20, 21, 24, 25, 26, 27, 29, 30, 32, 33, 35, 37, 39, 42, 45, 49, 53, 55, 57, 59, 62, 63, 64, 65, 69], "explicitli": [3, 8, 17, 29, 30, 31, 50, 53, 62, 64, 69], "domain": [3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 48, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "vector": [3, 6, 8, 11, 12, 13, 35, 36, 38, 40, 41, 43, 58, 62, 63], "minimum": [3, 11, 12, 14, 16, 21, 24, 25, 28, 29, 33, 35, 37, 39, 44, 53, 62, 64], "even": [3, 5, 20, 25, 29, 30, 39, 42, 48, 50, 53, 62, 63, 65, 66], "like": [3, 4, 8, 9, 11, 12, 14, 18, 29, 30, 31, 32, 37, 39, 42, 50, 52, 62, 63, 65, 66], "immedi": [3, 21, 29], "clear": [3, 9, 17, 36, 57, 63, 69], "what": [3, 8, 15, 21, 22, 25, 29, 31, 39, 41, 43, 46, 47, 51, 55, 57, 59, 62, 63, 64, 66, 68], "exactli": [3, 14, 33, 34, 35, 45, 50, 51, 53, 55, 62, 63, 66], "where": [3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 35, 37, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68, 69], "come": [3, 4, 14, 15, 30, 36, 42, 50, 63], "plai": [3, 8, 36, 46, 50, 53, 63], "thei": [3, 5, 8, 16, 18, 22, 24, 29, 30, 31, 32, 36, 37, 39, 42, 49, 51, 53, 57, 62, 63, 65, 66, 68, 69], "procedur": [3, 37, 55, 63], "long": [3, 4, 14, 16, 22, 25, 29, 46, 47, 60, 63, 69], "standard": [3, 5, 6, 8, 13, 14, 22, 35, 39, 41, 42, 50, 58, 62, 69], "fashion": [3, 4, 53], "practition": [3, 49], "often": [3, 4, 16, 21, 28, 32, 35, 51, 63, 66, 69], "boil": 3, "down": [3, 17, 23, 30, 35, 47, 62, 63, 64], "pass": [3, 4, 5, 18, 20, 21, 24, 28, 42, 50, 68], "softwar": [3, 26], "regardless": [3, 4, 8, 12, 18, 29, 46, 52, 60], "wa": [3, 7, 14, 25, 29, 30, 32, 35, 36, 37, 39, 45, 46, 47, 48, 49, 53, 55, 59, 63, 65], "stori": [3, 46, 47], "behind": 3, "To": [3, 5, 8, 18, 21, 22, 23, 24, 25, 27, 29, 30, 35, 37, 39, 42, 44, 45, 49, 50, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68], "do": [3, 4, 8, 20, 23, 25, 29, 30, 31, 33, 35, 39, 41, 45, 53, 55, 57, 62, 63, 65, 66, 68, 69], "interfac": [3, 4, 5, 14, 45, 69], "commun": [3, 5, 7, 20, 25, 27, 64], "adopt": [3, 8, 26, 32, 42, 44, 47, 55], "python": [3, 5, 8, 13, 17, 20, 21, 25, 29, 30, 32, 37, 40, 41, 42, 45, 50, 53, 57, 66, 68, 69], "base": [3, 5, 7, 12, 13, 19, 21, 26, 29, 32, 35, 40, 41, 42, 47, 49, 50, 51, 52, 57, 63, 65, 68, 69], "carri": [3, 24, 35], "ll": [4, 39], "revisit": [4, 16, 25, 43, 61], "time": [4, 5, 6, 8, 14, 18, 20, 23, 24, 25, 26, 27, 30, 31, 33, 35, 36, 37, 39, 40, 42, 45, 46, 49, 50, 51, 52, 53, 57, 59, 62, 63, 65, 66, 68, 69], "capabl": [4, 7, 26, 39, 55], "scale": [4, 7, 29, 30, 35, 37, 39, 42, 57, 60, 62, 63, 66], "enabl": [4, 5, 28, 29, 45, 50, 68], "vari": [4, 12, 38, 50, 52, 55, 57, 64], "addit": [4, 6, 7, 12, 15, 18, 21, 23, 25, 27, 37, 42, 45, 47, 49, 50, 59, 62, 63, 66, 68, 69], "compon": [4, 5, 8, 13, 14, 18, 22, 26, 38, 45, 50, 58, 69], "index": [4, 5, 8, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 35, 37, 39, 40, 41, 42, 44, 45, 49, 50, 52, 53, 57, 59, 62, 64, 65, 68], "essenti": [4, 22, 29, 30, 37, 42, 50, 53, 55, 63], "scalabl": [4, 6], "maintain": [4, 5, 8, 27, 29, 45, 66, 69], "more": [4, 5, 8, 10, 11, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 32, 35, 37, 39, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "analysi": [4, 7, 8, 12, 13, 21, 29, 32, 42, 46, 47, 50, 51, 53, 55, 62, 69], "examin": [4, 7, 17, 49], "identifi": [4, 5, 16, 18, 24, 27, 29, 31, 34, 37, 39, 42, 44, 45, 47, 50, 62, 66, 69], "underli": [4, 40, 63], "verifi": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 44, 46, 48, 50, 52, 53, 55, 57, 59, 60, 62, 66], "high": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 42, 44, 49, 50, 52, 55, 57, 59, 60, 63, 65, 66, 69], "via": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 38, 39, 44, 46, 48, 50, 51, 57, 60, 66], "appsi": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 35, 52, 60, 66], "modul": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "elsewher": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 35, 38, 39, 44, 46, 48, 52, 57, 60, 66, 69], "assum": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "cbc": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 35, 52, 53, 59, 60, 62, 63, 64, 65, 66, 68], "been": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 60, 62, 64, 66, 68, 69], "previous": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 35, 38, 39, 44, 46, 47, 48, 50, 52, 53, 57, 60, 62, 65, 66, 68, 69], "solverfactori": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "It": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 39, 44, 45, 46, 48, 52, 55, 57, 60, 63, 65, 66], "sy": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "pip": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "dev": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66], "null": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66], "highspi": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 52, 53, 59, 60, 62, 63, 64, 65, 66], "environ": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "appsi_high": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 53, 55, 59, 60, 62, 63, 64, 65, 66], "els": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 33, 34, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 60, 62, 63, 65, 66, 68, 69], "assert": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 55, 57, 60], "basic": [4, 16, 17, 21, 27, 42, 55, 65, 68, 69], "previou": [4, 9, 12, 15, 18, 28, 29, 35, 42, 45, 50, 51, 63], "were": [4, 18, 27, 30, 35, 42, 49, 62, 65], "distinct": [4, 22, 29], "evid": [4, 20], "compris": [4, 21, 23, 25, 31, 37, 40, 59, 68, 69], "abbrevi": [4, 29, 68], "m": [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "factor": [4, 7, 20, 31, 42, 44, 48, 50, 55, 62, 65, 69], "attribut": [4, 5, 7, 14, 29, 35, 37, 45, 65, 68, 69], "built": [4, 20, 57], "librari": [4, 5, 8, 13, 21, 30, 32, 33, 40, 41, 44, 45, 47, 49, 50, 69], "handl": [4, 23, 26, 45, 68], "tabular": [4, 5], "sever": [4, 5, 6, 7, 11, 16, 19, 24, 26, 28, 29, 36, 37, 39, 42, 49, 57, 69], "option": [4, 5, 14, 21, 27, 29, 33, 41, 42, 50, 63, 65, 68, 69], "would": [4, 7, 8, 12, 15, 17, 18, 19, 21, 25, 26, 29, 31, 32, 33, 35, 39, 42, 45, 48, 49, 50, 52, 53, 55, 57, 59, 62, 63, 64, 65, 66, 68], "appropri": [4, 5, 42, 50], "task": [4, 16, 20, 24, 29, 30, 32, 37, 42, 53], "nest": [4, 37, 63, 68, 69], "dictionari": [4, 18, 21, 29, 34, 35, 37, 42, 45, 50, 53, 57, 63, 69], "column": [4, 5, 7, 12, 14, 15, 18, 20, 22, 24, 25, 29, 30, 31, 32, 35, 39, 42, 45, 49, 50, 52, 53, 62, 64, 66, 69], "show": [4, 5, 7, 9, 12, 13, 14, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 62, 63, 66, 68, 69], "repres": [4, 6, 8, 18, 19, 22, 23, 25, 31, 33, 34, 35, 37, 39, 42, 44, 45, 46, 47, 49, 50, 57, 59, 68, 69], "kei": [4, 5, 8, 14, 20, 21, 29, 32, 33, 34, 35, 37, 40, 46, 49, 52, 53, 57, 59, 60, 63, 65, 66, 68, 69], "outermost": 4, "inner": [4, 42, 50], "float": [4, 30, 42, 50, 52, 60, 69], "none": [4, 5, 7, 20, 21, 27, 29, 30, 32, 34, 35, 40, 42, 45, 47, 50, 52, 57, 66, 68], "print": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68], "item": [4, 21, 30, 32, 34, 35, 37, 50, 53, 57, 59, 60, 65, 66, 69], "consum": [4, 21, 35, 57, 65, 69], "8s": [4, 29, 49], "row": [4, 5, 7, 8, 22, 29, 31, 35, 42, 53, 63, 66, 69], "label": [4, 7, 13, 15, 24, 27, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 45, 50, 52, 53, 57, 60, 66, 69], "4s": 4, "By": [4, 5, 7, 14, 30, 31, 32, 55, 69], "rearrang": [4, 42], "straightforward": [4, 18, 55, 69], "becom": [4, 8, 9, 14, 19, 20, 22, 25, 29, 38, 39, 41, 42, 45, 47, 49, 50, 57, 58, 59, 60, 65, 66], "collect": [4, 5, 6, 7, 11, 13, 15, 20, 21, 27, 31, 32, 33, 35, 40, 42, 50, 62, 63, 69], "compar": [4, 7, 8, 13, 14, 19, 20, 22, 29, 30, 37, 39, 40, 42, 45, 47, 50, 59, 60, 62, 64, 66], "adapt": [4, 15, 49, 57, 62, 63, 65], "let": [4, 7, 8, 9, 11, 12, 15, 19, 20, 21, 25, 27, 29, 30, 33, 34, 35, 37, 38, 39, 44, 45, 47, 50, 52, 55, 57, 58, 59, 62, 63, 65, 68], "cal": [4, 50], "p": [4, 11, 12, 18, 23, 24, 26, 33, 35, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 53, 57, 58, 60, 62, 65, 66, 68], "respect": [4, 5, 8, 14, 18, 21, 26, 27, 29, 30, 32, 34, 35, 37, 39, 42, 46, 55, 57, 62, 63, 64, 66, 68], "x_r": [4, 39], "y_p": 4, "denot": [4, 8, 12, 15, 18, 19, 21, 23, 26, 27, 29, 30, 31, 35, 37, 39, 40, 49, 53, 57, 62, 65, 69], "constrain": [4, 12, 15, 16, 29, 35, 39, 45, 46, 49], "zero": [4, 13, 19, 29, 35, 37, 40, 41, 42, 44, 45, 50, 52, 60, 63, 65, 66], "b_r": 4, "b_p": 4, "b_q": 4, "don": [4, 8, 29, 57, 66, 69], "insert": [4, 5, 32, 45, 47], "larger": [4, 8, 20, 27, 30, 33, 37, 42, 47, 50, 53, 59], "than": [4, 5, 8, 10, 12, 15, 16, 17, 20, 21, 23, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 39, 42, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 65], "ever": [4, 42, 50], "design": [4, 5, 14, 19, 22, 27, 32, 39, 40, 42, 43, 66, 68], "caus": [4, 5, 39, 68], "ignor": [4, 35, 42, 50, 57], "befor": [4, 13, 20, 21, 22, 30, 33, 39, 40, 42, 46, 53, 57, 59, 60, 62, 63, 65, 66], "sum_": [4, 7, 12, 13, 14, 15, 18, 20, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 57, 58, 59, 62, 63, 65, 66, 69], "c_p": 4, "c_r": 4, "a_": [4, 15, 25, 29, 31, 37], "put": [4, 42, 59, 63, 65], "piec": [4, 21, 37], "flexibl": [4, 32, 35, 36, 63, 68], "particular": [4, 14, 16, 21, 25, 30, 33, 35, 37, 39, 40, 45, 55, 62, 63, 65, 66, 69], "hold": [4, 5, 8, 9, 12, 14, 16, 18, 24, 27, 29, 35, 45, 52, 57, 59, 60, 62, 63, 65, 66], "scienc": [4, 5, 25, 32, 44, 45, 46, 62, 64], "see": [4, 5, 20, 21, 25, 26, 30, 31, 40, 44, 45, 46, 48, 50, 55, 57, 60, 63, 64, 65, 66, 68], "facilit": [4, 8, 14, 69], "construct": [4, 5, 7, 9, 14, 18, 21, 29, 32, 37, 38, 42, 44, 45, 50, 53, 65, 66, 68, 69], "pyo": [4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "initi": [4, 7, 8, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 46, 48, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "assign": [4, 5, 15, 16, 19, 22, 24, 25, 29, 30, 31, 32, 33, 37, 41, 42, 50, 51, 66], "decor": [4, 5, 8, 9, 25, 32, 62], "declar": [4, 5, 35, 65, 66, 69], "return": [4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "form": [4, 6, 22, 23, 36, 44, 45, 51, 58, 60, 63, 65, 68], "param": [4, 7, 12, 14, 15, 18, 21, 22, 23, 24, 25, 27, 29, 30, 32, 39, 42, 52, 57, 60, 65, 68, 69], "omit": [4, 69], "emb": 4, "extern": [4, 21, 44, 55], "directli": [4, 5, 7, 14, 22, 23, 32, 35, 44, 45, 50, 59], "effect": [4, 5, 21, 23, 34, 44, 46, 47, 53, 68], "doe": [4, 5, 15, 21, 23, 25, 27, 29, 30, 35, 37, 40, 42, 45, 50, 55, 62, 66], "keep": [4, 12, 18, 25, 33, 35, 39, 50, 53, 63, 65, 69], "shorter": 4, "remov": [4, 6, 8, 15, 29, 37, 42, 53], "overhead": 4, "blur": 4, "boundari": [4, 27, 69], "statement": [4, 30, 32, 62], "edit": [4, 37, 46], "locat": [4, 16, 24, 29, 32, 34, 39, 41, 42, 57, 59, 69], "portion": [4, 49], "therebi": 4, "significantli": [4, 8, 27, 30, 39, 42, 50], "improv": [4, 5, 25, 39, 42, 44, 45, 47, 64], "maintainabi": 4, "concern": [4, 30], "overkil": 4, "small": [4, 5, 8, 12, 25, 26, 29, 30, 31, 33, 34, 37, 39, 41, 63, 65, 69], "consider": [4, 14, 15, 21, 25, 32, 42, 59, 69], "note": [4, 5, 9, 11, 12, 13, 14, 15, 17, 18, 20, 24, 25, 32, 33, 34, 35, 37, 40, 41, 42, 48, 55, 57, 60, 62, 66, 68, 69], "becaus": [4, 8, 11, 18, 21, 25, 27, 29, 30, 32, 35, 37, 39, 42, 45, 50, 53, 55, 57, 63, 65, 68, 69], "take": [4, 5, 7, 8, 9, 11, 16, 17, 18, 21, 22, 23, 24, 27, 29, 31, 33, 35, 38, 39, 42, 45, 47, 48, 50, 51, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "logic": [4, 5, 8, 12, 17, 18, 19, 22, 26, 29, 52, 55, 69], "def": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "coeffici": [4, 6, 7, 8, 13, 15, 17, 18, 29, 40, 42, 44, 50, 55, 62, 63], "cp": [4, 41], "cr": 4, "argumentn": 4, "var": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 48, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "fix": [4, 5, 6, 7, 12, 14, 24, 25, 27, 30, 32, 35, 40, 44, 45, 46, 47, 49, 57, 60, 62, 63, 64, 65, 66, 68], "done": [4, 5, 21, 22, 39, 42, 59, 63], "parlanc": 4, "sometim": [4, 36, 46, 58], "call": [4, 8, 24, 27, 29, 31, 32, 35, 38, 39, 40, 42, 48, 49, 50, 53, 59, 62, 66, 68], "rule": [4, 12, 29, 39, 45, 60, 61, 63, 65, 69], "lambda": [4, 18, 19, 20, 21, 22, 25, 27, 29, 31, 35, 39, 42, 44, 46, 47, 49, 50, 52, 53, 55, 57, 60, 65, 66, 68, 69], "argument": [4, 5, 18, 33, 39, 42, 50, 55, 62, 63, 65, 68, 69], "member": [4, 30, 32], "tupl": [4, 5, 8, 21, 25, 29, 37, 68], "quicksum": [4, 12, 18, 30, 33, 52, 55], "accept": [4, 5, 21, 22, 29, 32, 42, 46, 49, 57, 63, 69], "success": [4, 7, 47, 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26, 27, 29, 30, 32, 33, 34, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 67, 69], "evalu": [2, 13, 42, 50, 63], "specif": [2, 3, 5, 6, 8, 10, 13, 14, 15, 17, 20, 25, 29, 30, 34, 35, 37, 39, 41, 42, 45, 48, 53, 55, 57, 59, 60, 62, 63, 65, 67, 68, 69], "i": [2, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 66, 69], "e": [2, 7, 18, 19, 21, 22, 25, 27, 29, 30, 32, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 47, 49, 50, 53, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "valu": [2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 66, 68, 69], "earlier": [2, 5, 10, 21, 42, 45, 48, 52, 57, 59], "For": [2, 3, 5, 8, 10, 14, 16, 18, 20, 21, 22, 24, 27, 29, 30, 31, 34, 35, 36, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "specifi": [2, 4, 5, 8, 13, 21, 24, 27, 29, 30, 31, 34, 37, 38, 39, 42, 45, 46, 48, 50, 58, 66, 68, 69], "either": [2, 3, 4, 5, 20, 21, 22, 23, 24, 26, 27, 29, 35, 50, 59, 63, 65, 69], "maxim": [2, 3, 4, 5, 6, 8, 9, 10, 17, 18, 20, 23, 26, 29, 30, 31, 35, 37, 38, 39, 41, 46, 47, 48, 49, 55, 58, 60, 62, 63, 64, 68, 69], "minim": [2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 18, 20, 21, 22, 24, 25, 27, 29, 33, 34, 35, 37, 40, 42, 44, 45, 50, 52, 53, 55, 57, 64, 65, 66, 69], "In": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69], "oper": [2, 3, 15, 21, 22, 27, 29, 35, 37, 39, 41, 42, 44, 45, 53, 59, 62, 63, 65, 66, 68], "cost": [2, 3, 4, 5, 6, 11, 12, 14, 15, 18, 20, 26, 28, 29, 30, 31, 33, 35, 37, 39, 41, 44, 45, 52, 53, 57, 59, 60, 63, 64, 65, 66, 68], "number": [2, 3, 4, 5, 8, 9, 10, 13, 16, 17, 18, 19, 20, 22, 24, 25, 27, 29, 31, 33, 35, 37, 38, 40, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69], "satisfi": [2, 3, 9, 15, 16, 18, 19, 20, 27, 29, 30, 31, 32, 34, 39, 42, 46, 47, 49, 57, 59, 62, 65], "custom": [2, 20, 21, 29, 32, 37, 39, 42, 51, 57, 62, 69], "restrict": [2, 16, 25, 30, 33, 35, 46, 49, 53, 55, 68, 69], "possibl": [2, 4, 5, 6, 9, 13, 15, 16, 17, 18, 19, 20, 21, 24, 27, 29, 30, 32, 33, 34, 35, 38, 39, 40, 42, 47, 50, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69], "condit": [2, 3, 8, 15, 18, 23, 24, 26, 27, 29, 30, 39, 42, 44, 50, 55, 59, 64, 68, 69], "must": [2, 3, 5, 19, 21, 23, 26, 27, 29, 31, 32, 35, 38, 39, 44, 53, 63, 64, 65, 66, 68], "requir": [2, 3, 4, 8, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 37, 39, 45, 47, 52, 53, 57, 59, 62, 63, 64, 66, 68, 69], "maximum": [2, 3, 8, 11, 15, 18, 23, 24, 25, 29, 33, 34, 35, 39, 44, 47, 48, 49, 53, 55, 57, 63, 66, 68], "allow": [2, 4, 8, 18, 23, 24, 27, 29, 31, 32, 35, 41, 45, 48, 49, 53, 55, 57, 65, 68], "budget": [2, 12, 37, 52, 63], "demand": [2, 3, 4, 6, 18, 20, 26, 30, 32, 34, 35, 37, 39, 45, 51, 52, 57, 59, 63, 64, 65, 66, 68, 69], "import": [2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 58, 59, 60, 63, 64, 69], "met": [2, 35, 39, 57], "capac": [2, 12, 18, 23, 24, 30, 34, 35, 41, 52, 57, 62, 66, 69], "warehous": [2, 18, 45, 51, 60, 69], "exceed": [2, 29, 30, 39, 57], "both": [2, 4, 5, 8, 12, 13, 17, 20, 23, 24, 26, 27, 29, 33, 35, 37, 38, 39, 42, 45, 47, 50, 61, 62, 63], "express": [2, 3, 4, 7, 8, 9, 10, 11, 12, 16, 18, 19, 22, 26, 29, 30, 32, 34, 35, 39, 41, 42, 44, 45, 46, 49, 50, 52, 55, 57, 60, 64, 65, 66, 68, 69], "defin": [2, 4, 5, 8, 9, 12, 13, 14, 16, 20, 22, 25, 26, 27, 32, 33, 35, 37, 39, 40, 41, 42, 45, 46, 50, 53, 55, 57, 62, 63, 65, 66, 68, 69], "feasibl": [2, 5, 8, 9, 17, 20, 30, 35, 37, 41, 44, 46, 47, 49, 53, 60, 63, 65, 66], "region": [2, 8, 20, 32, 35], "set": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 44, 45, 46, 47, 48, 49, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "candid": [2, 3, 7, 21, 37], "meet": [2, 3, 5, 12, 18, 22, 25, 29, 30, 32, 35, 37, 39, 43, 52, 57, 59, 65, 66], "best": [2, 5, 7, 8, 29, 30, 35, 44, 57, 63, 66, 69], "global": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 44, 46, 48, 52, 55, 57, 60, 62, 66, 69], "optimum": [2, 39, 41, 44], "among": [2, 3, 7, 11, 14, 15, 21, 22, 26, 31, 32, 33, 47, 48, 49, 62, 64, 65, 69], "appli": [2, 4, 5, 18, 24, 35, 37, 39, 42, 44, 45, 49, 65, 66, 68], "type": [2, 3, 4, 5, 6, 8, 12, 16, 17, 19, 21, 25, 29, 30, 35, 37, 42, 45, 50, 52, 55, 57, 65, 66, 68], "relat": [2, 5, 18, 23, 26, 29, 33, 50, 55, 57, 62, 63, 65], "fundament": [2, 14, 39, 68], "question": [2, 8, 15, 22, 29, 42, 45, 51, 59, 64, 65], "translat": [2, 4, 5, 18, 22, 29, 32, 37, 44], "real": [2, 4, 5, 7, 13, 16, 21, 30, 31, 35, 36, 37, 40, 46, 47, 49, 51, 53, 55, 57, 59, 62, 63, 65], "abstract": [2, 4, 8, 68], "represent": [2, 21, 42, 44, 50], "Not": [2, 29], "aspect": [2, 6, 8, 14, 16, 28, 36, 43, 54, 56, 61], "taken": [2, 29, 33, 63, 65, 69], "account": [2, 10, 18, 23, 24, 29, 31, 35, 43, 46, 47, 55, 59, 60, 63, 65, 66, 68], "so": [2, 3, 4, 5, 8, 9, 13, 18, 21, 23, 24, 25, 27, 29, 30, 35, 36, 37, 38, 39, 40, 42, 44, 48, 50, 51, 53, 55, 57, 62, 63, 66, 68], "mani": [2, 3, 4, 8, 16, 19, 20, 22, 23, 27, 29, 30, 31, 33, 37, 42, 45, 46, 47, 49, 50, 52, 53, 55, 59, 62, 63, 65, 66, 69], "made": [2, 3, 10, 12, 18, 20, 24, 29, 52, 59, 63, 66], "step": [2, 3, 4, 8, 9, 12, 14, 15, 18, 21, 29, 45, 46, 52, 53, 62, 63, 68, 69], "typic": [2, 21, 35, 57, 59, 63, 68, 69], "signific": [2, 5, 8, 41, 45, 46, 47, 49, 50], "impact": [2, 7, 39, 51, 64], "approach": [2, 5, 7, 8, 10, 13, 14, 17, 19, 20, 22, 26, 27, 30, 33, 37, 39, 44, 46, 49, 57, 63, 65, 68], "There": [2, 5, 18, 19, 22, 25, 26, 29, 30, 35, 37, 39, 44, 45, 59, 63, 68, 69], "multipl": [2, 3, 12, 15, 18, 27, 29, 31, 32, 34, 37, 39, 69], "equival": [2, 5, 8, 18, 20, 22, 33, 42, 44, 45, 53, 55, 58, 62, 69], "formul": [2, 3, 4, 6, 8, 9, 11, 13, 14, 15, 16, 18, 22, 23, 26, 27, 28, 29, 30, 32, 35, 36, 39, 40, 44, 49, 51, 55, 57, 59, 60, 62, 65, 66, 69], "conceptu": 2, "same": [2, 3, 4, 5, 10, 11, 13, 14, 15, 18, 19, 21, 22, 25, 27, 29, 30, 31, 32, 33, 34, 40, 42, 45, 46, 50, 53, 55, 57, 60, 63, 65, 66, 68, 69], "comput": [2, 4, 5, 7, 8, 14, 15, 18, 22, 23, 29, 30, 31, 35, 37, 39, 42, 45, 46, 49, 50, 52, 59, 62, 64, 65, 66, 68, 69], "complex": [2, 4, 5, 15, 21, 22, 23, 29, 31, 37, 68, 69], "mai": [2, 3, 4, 5, 10, 11, 12, 15, 16, 17, 18, 20, 21, 23, 27, 29, 31, 32, 35, 37, 39, 41, 42, 45, 46, 50, 52, 55, 57, 58, 64, 68], "differ": [2, 3, 5, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 27, 29, 30, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 45, 48, 49, 50, 51, 53, 55, 57, 59, 60, 63, 64, 65, 66, 69], "interpret": [2, 4, 15, 33, 41], "s": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "after": [2, 5, 13, 23, 29, 30, 31, 40, 47, 53, 55, 59, 63, 64, 65, 66, 68], "ha": [2, 3, 4, 5, 7, 10, 12, 14, 18, 21, 22, 24, 25, 26, 27, 29, 30, 31, 33, 35, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68], "back": [2, 13, 23, 29, 31, 33, 42, 50, 63, 68], "origin": [2, 3, 4, 5, 8, 9, 10, 13, 14, 17, 25, 27, 30, 35, 37, 39, 45, 48], "These": [2, 4, 15, 25, 27, 29, 34, 35, 39, 42, 45, 47, 49, 53, 57, 59, 62, 68, 69], "treat": [2, 21, 30, 39, 51, 66], "continu": [2, 12, 18, 22, 23, 39, 42, 44, 50, 52, 60, 66], "process": [2, 4, 23, 29, 39, 41, 42, 45, 50, 53, 55, 68, 69], "sequenti": 2, "final": [2, 4, 5, 12, 14, 21, 22, 23, 29, 31, 39, 45, 62, 65], "turn": [2, 3, 16, 21, 30, 36, 42, 50, 53, 57, 66], "out": [2, 3, 23, 24, 27, 29, 30, 32, 36, 37, 53, 57, 65, 66], "impract": [2, 29], "adjust": [2, 4, 14, 29, 35, 41, 57, 62, 65, 66], "certain": [2, 16, 29, 30, 32, 42, 45, 50, 55, 57, 62, 66], "desir": [2, 3, 12, 18, 25, 30, 36, 52, 68], "properti": [2, 8, 30, 36, 44, 46, 48, 49, 57], "cannot": [2, 8, 12, 16, 21, 22, 25, 29, 33, 35, 44, 52, 53, 60, 62, 63, 66], "effici": [2, 10, 14, 21, 27, 29, 30, 48, 49, 50, 55, 69], "perhap": [2, 19, 32, 37], "re": [2, 69], "includ": [2, 5, 6, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 29, 31, 32, 36, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 53, 55, 57, 58, 62, 63, 64, 65, 66, 67, 68, 69], "well": [2, 5, 7, 13, 14, 19, 22, 27, 36, 37, 44, 46, 47, 60, 64, 69], "except": [2, 20, 25, 33, 66, 68, 69], "mathematician": 2, "studi": [2, 15, 21, 27, 29, 37, 39, 44, 57, 60, 69], "alwai": [2, 4, 10, 12, 17, 24, 35, 38, 40, 42, 46, 47, 48, 50, 51, 55, 58, 62, 68], "flaw": 2, "challeng": [2, 8, 19, 27, 31, 37, 39, 42], "follow": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "given": [2, 3, 4, 5, 7, 8, 9, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 35, 37, 39, 42, 44, 45, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "f": [2, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "x": [2, 4, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 47, 48, 50, 52, 53, 55, 57, 58, 59, 60, 63, 64, 65, 66, 68, 69], "mathbb": [2, 6, 8, 13, 16, 17, 18, 26, 35, 37, 38, 40, 42, 45, 46, 47, 49, 50, 55, 57, 58, 59, 60, 62, 65, 66], "r": [2, 4, 6, 8, 13, 14, 16, 18, 19, 21, 22, 24, 25, 27, 29, 31, 32, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 58, 59, 60, 62, 63, 64, 65, 66, 68], "subseteq": [2, 16, 33, 35, 53], "n": [2, 6, 7, 8, 9, 13, 16, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 60, 62, 63, 69], "being": [2, 5, 6, 8, 33, 35, 38, 39, 50, 53, 66], "y": [2, 4, 7, 8, 9, 13, 14, 18, 19, 20, 23, 24, 26, 27, 29, 30, 31, 32, 34, 35, 38, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 55, 57, 59, 60, 63, 64, 66, 68, 69], "geq": [2, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 55, 57, 58, 60, 62, 63, 65, 66, 68], "foral": [2, 4, 7, 11, 12, 13, 14, 15, 18, 19, 20, 22, 23, 24, 25, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 45, 46, 48, 49, 50, 53, 55, 57, 59, 62, 63, 65, 66], "least": [2, 6, 7, 12, 18, 22, 24, 33, 35, 36, 37, 39, 52, 53, 63, 64], "good": [2, 4, 5, 7, 15, 20, 27, 29, 33, 34, 38, 46, 49, 59, 63, 64, 69], "similarli": [2, 8, 13, 18, 35, 40], "chang": [2, 4, 10, 14, 15, 21, 23, 24, 27, 29, 30, 31, 32, 33, 35, 38, 39, 40, 41, 48, 51, 53, 55, 57, 58, 62, 63, 65, 68, 69], "last": [2, 12, 18, 22, 23, 24, 38, 39, 52, 53, 55, 64, 66], "leq": [2, 3, 4, 8, 9, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 62, 63, 65, 66, 69], "case": [2, 3, 4, 5, 7, 8, 13, 16, 20, 21, 25, 26, 27, 29, 30, 32, 37, 38, 39, 40, 42, 46, 47, 49, 50, 55, 57, 59, 60, 66, 68, 69], "refer": [2, 3, 4, 6, 8, 13, 16, 20, 24, 27, 29, 32, 34, 39, 40, 42, 47, 50, 65, 69], "begin": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "align": [2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "min": [2, 6, 7, 8, 9, 11, 13, 14, 16, 18, 20, 22, 24, 25, 27, 29, 30, 32, 33, 34, 35, 37, 39, 40, 42, 44, 45, 46, 50, 53, 55, 57, 59, 60, 63, 65, 66, 69], "quad": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 58, 59, 60, 62, 63, 65, 68, 69], "text": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "t": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "end": [2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "lead": [2, 14, 17, 18, 19, 20, 21, 22, 26, 29, 36, 39, 42, 44, 50, 55, 57, 63, 66, 69], "techniqu": [2, 7, 11, 13, 21, 22, 23, 26, 32, 42, 45, 49, 57, 63, 65], "introductori": [2, 61], "present": [2, 4, 5, 7, 8, 13, 14, 24, 29, 31, 32, 35, 37, 39, 40, 41, 42, 46, 47, 48, 49, 50, 53, 62, 64, 66, 68, 69], "simpl": [2, 3, 4, 5, 12, 21, 26, 30, 31, 36, 37, 39, 41, 42, 45, 50, 55, 68, 69], "context": [2, 15, 25, 33, 34, 58, 63, 66], "plan": [2, 4, 5, 10, 11, 15, 16, 18, 24, 25, 27, 45, 51, 59, 61], "explain": [2, 7, 35, 39, 50, 57, 66], "structur": [2, 4, 8, 17, 26, 28, 29, 30, 37, 44, 62, 63, 65, 66, 68, 69], "formal": [2, 16], "implement": [2, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 22, 24, 27, 28, 29, 32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 51, 54, 56, 57, 58, 59, 61, 62, 63, 68, 69], "second": [2, 4, 5, 10, 13, 18, 21, 27, 29, 31, 32, 33, 35, 37, 38, 39, 42, 50, 60, 61, 62, 63, 64, 65, 66], "also": [2, 3, 4, 5, 8, 11, 12, 14, 15, 18, 20, 22, 23, 25, 29, 30, 35, 36, 38, 39, 41, 42, 45, 53, 55, 58, 62, 63, 65, 66, 69], "serv": [2, 4, 5, 20, 34, 53, 63], "tutori": [2, 25, 37, 46, 47, 69], "lastli": [2, 3, 62, 63, 66], "discuss": [2, 32, 42, 45, 50, 51, 63], "some": [2, 3, 4, 5, 7, 8, 13, 16, 21, 23, 27, 29, 30, 32, 33, 35, 39, 40, 41, 42, 44, 46, 47, 49, 50, 55, 57, 63, 65, 66, 68, 69], "advanc": [2, 3, 5, 23, 39, 45, 51, 63, 65, 66], "featur": [2, 4, 5, 6, 8, 13, 16, 20, 21, 22, 23, 27, 34, 39, 40, 47, 49, 60, 62, 68, 69], "third": [2, 4, 5, 32], "go": [2, 6, 8, 13, 14, 16, 21, 28, 30, 35, 36, 39, 40, 43, 51, 53, 54, 56, 63, 64, 65, 68], "next": [2, 3, 4, 5, 6, 7, 8, 12, 15, 16, 18, 21, 22, 23, 25, 28, 29, 30, 32, 34, 36, 38, 43, 46, 50, 51, 53, 54, 56, 57, 60, 64, 65, 66], "about": [2, 6, 8, 16, 20, 24, 28, 29, 30, 36, 43, 51, 54, 56, 57, 59, 62, 63, 65], "linear": [2, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 22, 23, 26, 29, 31, 35, 36, 39, 40, 41, 55, 57, 60, 61, 62, 63, 65], "compani": [3, 6, 8, 12, 17, 18, 34, 39, 45, 51, 52, 53, 55, 63], "produc": [3, 4, 7, 8, 10, 12, 15, 17, 21, 23, 26, 29, 31, 32, 35, 37, 39, 42, 46, 47, 52, 53, 55, 57, 63, 65, 66, 68], "two": [3, 4, 5, 6, 8, 12, 13, 14, 16, 17, 19, 20, 21, 23, 25, 26, 29, 30, 31, 32, 33, 37, 39, 42, 45, 47, 50, 53, 55, 56, 57, 59, 60, 65, 68, 69], "version": [3, 4, 5, 10, 18, 20, 30, 35, 39, 45, 53, 54, 55, 63, 65, 66, 69], "each": [3, 4, 5, 8, 9, 12, 13, 14, 18, 19, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 42, 46, 47, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "raw": [3, 5, 8, 12, 18, 26, 29, 35, 39, 42, 50, 52, 57, 63, 65, 66], "10": [3, 4, 5, 7, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "per": [3, 8, 10, 12, 14, 18, 23, 24, 25, 26, 29, 32, 34, 37, 44, 45, 52, 60, 63, 64, 65], "gram": [3, 18, 42, 50], "special": [3, 4, 11, 12, 13, 16, 28, 30, 37, 40, 45, 62, 69], "labor": [3, 4, 26, 63, 68], "finish": [3, 12, 18, 21, 22, 23, 26, 37, 52, 53, 69], "u": [3, 4, 5, 14, 18, 23, 29, 34, 42, 44, 45, 46, 49, 50, 53, 55, 57, 63, 68, 69], "higher": [3, 14, 26, 29, 39, 42, 47, 50, 52, 57, 59, 63, 65], "270": [3, 4, 5, 26, 29, 63, 66, 68], "unit": [3, 4, 5, 10, 12, 14, 15, 18, 23, 24, 26, 29, 31, 32, 34, 35, 39, 44, 45, 47, 52, 57, 58, 59, 60, 62, 63, 64, 65, 68], "one": [3, 4, 5, 6, 8, 9, 13, 14, 15, 17, 18, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 62, 63, 64, 65, 66], "hour": [3, 4, 21, 24, 25, 26, 53, 63], "b": [3, 4, 5, 6, 7, 8, 13, 15, 16, 18, 19, 21, 22, 25, 26, 29, 32, 34, 35, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 53, 60, 62, 63, 65, 66, 68, 69], "due": [3, 4, 12, 14, 18, 29, 35, 38, 39, 51, 52, 55, 59, 62, 64, 65, 69], "market": [3, 4, 14, 15, 29, 31, 39, 46, 47, 49, 62, 63, 64], "limit": [3, 5, 12, 18, 20, 21, 24, 25, 26, 29, 32, 35, 37, 39, 41, 44, 46, 49, 52, 57, 63, 65, 66, 69], "40": [3, 4, 5, 7, 24, 25, 26, 29, 32, 33, 37, 44, 45, 46, 59, 62, 63, 64, 68, 69], "week": [3, 25, 29, 33, 62], "v": [3, 4, 5, 14, 20, 21, 24, 29, 30, 33, 34, 35, 39, 42, 45, 46, 50, 53, 57, 63, 65, 66, 68, 69], "lower": [3, 4, 5, 12, 14, 21, 29, 31, 32, 37, 39, 40, 55, 59, 62, 64, 65, 69], "unlimit": [3, 4, 26, 37, 63], "210": [3, 4, 5, 26, 62, 63, 64, 68], "9": [3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 41, 42, 45, 50, 51, 52, 53, 55, 62, 63, 66, 68], "1": [3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 37, 38, 40, 41, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 61, 63, 65, 66, 68, 69], "summar": [3, 4, 25, 32, 35, 39, 42, 50, 59, 62, 63, 64], "tabl": [3, 4, 18, 21, 22, 24, 26, 27, 31, 42, 46, 52, 53, 55, 59, 60, 62, 64, 69], "g": [3, 4, 8, 14, 18, 20, 22, 27, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 44, 45, 50, 53, 55, 60, 65, 66, 68], "hr": [3, 4, 24, 53], "2": [3, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 37, 38, 40, 41, 42, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 63, 65, 66, 68, 69], "weekli": [3, 25], "avail": [3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 66, 68], "inventori": [3, 12, 18, 29, 45, 52, 59, 60], "shelf": 3, "life": [3, 22, 30, 36, 44, 53], "order": [3, 4, 10, 12, 18, 21, 22, 25, 30, 32, 35, 37, 41, 42, 43, 50, 52, 53, 59, 63], "left": [3, 7, 8, 9, 10, 12, 13, 21, 22, 23, 24, 25, 27, 30, 32, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 57, 60, 62, 63, 65], "over": [3, 4, 10, 11, 14, 18, 21, 23, 25, 29, 30, 35, 37, 39, 41, 42, 45, 47, 50, 52, 59, 62, 63, 64, 68, 69], "discard": 3, "detail": [3, 8, 20, 25, 42, 44, 50, 59], "resourc": [3, 4, 15, 21, 25, 27, 29, 30, 37, 52, 64, 65, 68], "amount": [3, 4, 12, 15, 16, 17, 18, 21, 22, 25, 29, 31, 32, 34, 38, 39, 51, 52, 55, 57, 58, 60, 63, 64, 65, 69], "80": [3, 4, 5, 26, 29, 32, 35, 41, 47, 49, 50, 63, 64, 66, 68], "50": [3, 4, 5, 9, 14, 18, 24, 26, 29, 31, 32, 35, 37, 39, 42, 44, 45, 52, 55, 60, 62, 63, 64, 66, 68, 69], "100": [3, 4, 5, 10, 18, 19, 20, 22, 24, 26, 29, 31, 32, 35, 37, 38, 39, 41, 42, 45, 47, 49, 50, 52, 55, 57, 60, 62, 63, 64, 65, 66, 68, 69], "want": [3, 14, 17, 18, 20, 29, 32, 33, 38, 40, 42, 48, 55, 58, 62, 63, 69], "its": [3, 5, 7, 8, 9, 13, 14, 20, 22, 30, 34, 37, 40, 42, 45, 50, 55, 63, 65, 68, 69], "gross": [3, 46, 47, 49], "profit": [3, 4, 5, 6, 8, 9, 10, 17, 23, 26, 29, 32, 37, 39, 41, 55, 62, 63, 64, 68, 69], "much": [3, 8, 12, 13, 17, 18, 23, 24, 27, 30, 33, 37, 44, 47, 51, 63, 65, 66], "abov": [3, 4, 6, 8, 11, 12, 13, 14, 17, 18, 22, 23, 24, 29, 30, 32, 33, 35, 37, 40, 44, 45, 46, 48, 49, 50, 52, 55, 57, 60, 62, 63, 65, 69], "optim": [3, 4, 5, 9, 10, 11, 13, 17, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 41, 45, 46, 52, 53, 55, 57, 59, 61, 67, 69], "reformul": [3, 10, 13, 14, 44, 46, 47, 49, 50, 55, 62], "involv": [3, 5, 6, 8, 11, 21, 31, 39, 42, 45, 46, 47, 49], "few": [3, 4, 5, 29, 32, 33, 42, 62, 68], "crucial": [3, 35], "element": [3, 4, 5, 8, 25, 30, 32, 42, 44, 47, 50, 65, 68, 69], "start": [3, 5, 7, 8, 13, 14, 18, 21, 22, 23, 24, 27, 29, 31, 33, 37, 49, 55, 62, 63], "point": [3, 4, 7, 8, 13, 16, 20, 23, 27, 29, 34, 39, 40, 41, 42, 45, 47, 50, 55, 60, 62, 66, 69], "list": [3, 4, 8, 14, 19, 21, 24, 25, 26, 29, 30, 31, 33, 35, 37, 42, 44, 46, 49, 50, 52, 53, 57, 60, 62, 63, 65, 68, 69], "relev": [3, 4, 18, 20, 27, 29, 66, 68, 69], "hand": [3, 4, 8, 9, 17, 20, 24, 25, 29, 30, 31, 42, 50, 55, 57, 59], "quantiti": [3, 8, 11, 12, 18, 34, 35, 37, 39, 43, 51, 52, 55, 63], "modifi": [3, 5, 17, 20, 21, 23, 29, 31, 42, 55, 57, 62, 65, 66, 68, 69], "achiev": [3, 11, 14, 23, 25, 38, 42, 50, 65, 68], "outcom": [3, 15, 32, 42, 46, 50, 57, 59, 63], "while": [3, 5, 8, 9, 12, 14, 17, 18, 20, 21, 24, 25, 26, 29, 33, 34, 35, 37, 42, 48, 49, 50, 51, 52, 53, 55, 57, 59, 62, 63, 65, 66], "stage": [3, 5, 27, 39, 46, 47, 60, 64, 65, 68, 69], "prove": [3, 8], "redund": [3, 69], "later": [3, 4, 5, 15, 21, 24, 27, 45, 47, 66, 69], "creat": [3, 12, 13, 14, 15, 19, 21, 22, 23, 27, 29, 30, 31, 33, 37, 39, 42, 45, 46, 49, 50, 57, 59, 62, 63, 64, 68, 69], "comprehens": [3, 7, 42, 50], "below": [3, 5, 9, 11, 12, 14, 17, 20, 21, 24, 29, 30, 35, 37, 39, 42, 44, 45, 46, 50, 55, 57, 60, 62, 63, 66, 69], "symbol": [3, 14, 22, 29, 31, 32, 49, 59, 68, 69], "descript": [3, 15, 21, 32, 42, 51, 55, 66], "upper": [3, 4, 5, 9, 12, 14, 21, 22, 23, 24, 29, 32, 33, 37, 38, 39, 40, 44, 45, 52, 55, 60, 68, 69], "bound": [3, 4, 5, 9, 14, 19, 21, 22, 23, 24, 26, 29, 30, 31, 33, 37, 38, 39, 42, 44, 53, 55, 57, 63, 64, 66, 68], "known": [3, 4, 5, 7, 13, 14, 19, 21, 22, 23, 27, 33, 38, 39, 40, 42, 44, 45, 47, 49, 50, 53, 57, 59, 63, 64, 65, 66], "x_m": [3, 5, 60], "0": [3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "x_a": [3, 5], "x_b": [3, 5], "y_u": [3, 5], "y_v": [3, 5], "measur": [3, 7, 10, 14, 23, 24, 25, 29, 39, 42, 50, 51], "max": [3, 4, 7, 8, 9, 10, 11, 14, 15, 17, 21, 22, 23, 24, 25, 26, 27, 29, 35, 37, 38, 39, 41, 42, 44, 46, 47, 48, 50, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "equal": [3, 5, 6, 7, 8, 10, 12, 15, 16, 23, 25, 26, 27, 29, 30, 32, 33, 34, 38, 39, 40, 41, 44, 45, 46, 47, 49, 53, 55, 57, 59, 60, 62, 63, 65, 66], "between": [3, 4, 5, 8, 10, 13, 14, 20, 21, 24, 25, 27, 29, 31, 32, 34, 35, 36, 38, 39, 40, 42, 44, 46, 47, 48, 50, 53, 57, 64, 65, 66, 68, 69], 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10, 16, 27, 51, 57], "simplifi": [3, 5, 24, 27, 50, 62, 68, 69], "relationship": [3, 5, 13, 22, 24, 25, 27, 29, 31, 44, 45, 46, 69], "inequ": [3, 6, 8, 9, 39, 47, 55, 65], "overal": [3, 8, 15, 25, 39, 44], "now": [3, 4, 5, 7, 8, 12, 14, 18, 20, 21, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 42, 45, 46, 47, 48, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "readi": [3, 29, 31, 45, 50, 63], "full": [3, 7, 13, 20, 23, 24, 32, 37, 39, 40, 42, 44, 49, 50, 55, 62, 63, 69], "canon": [3, 6, 38], "nonumb": [3, 4, 30], "textbook": [3, 20, 63, 64], "customari": [3, 8, 50], "under": [3, 4, 5, 14, 15, 18, 20, 25, 26, 31, 42, 52, 57, 59, 62, 63, 64, 68], "clearli": [3, 4, 7, 18, 20, 23, 25, 39, 53, 63, 66], "distinguish": [3, 29, 66, 69], "paramet": [3, 4, 5, 18, 21, 23, 32, 33, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 55, 57, 59, 60, 62, 63, 65, 66, 68], "might": [3, 15, 16, 27, 29, 31, 33, 35, 36, 39, 42, 51, 59, 65, 68], "letter": [3, 19, 45, 63], "throughout": [3, 5, 8, 29, 63, 69], "websit": 3, "howev": [3, 4, 8, 13, 15, 16, 17, 18, 20, 28, 29, 30, 31, 33, 35, 36, 39, 42, 44, 45, 48, 49, 50, 53, 55, 57, 59, 62, 63, 65, 66, 69], "stick": 3, "convent": [3, 5, 6, 8, 57, 65, 66], "onli": [3, 4, 7, 8, 9, 16, 18, 20, 21, 24, 25, 26, 27, 29, 30, 32, 33, 35, 37, 39, 42, 45, 49, 53, 55, 57, 59, 62, 63, 64, 65, 69], "explicitli": [3, 8, 17, 29, 30, 31, 50, 53, 62, 64, 69], "domain": [3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 48, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "vector": [3, 6, 8, 11, 12, 13, 35, 36, 38, 40, 41, 43, 58, 62, 63], "minimum": [3, 11, 12, 14, 16, 21, 24, 25, 28, 29, 33, 35, 37, 39, 44, 53, 62, 64], "even": [3, 5, 20, 25, 29, 30, 39, 42, 48, 50, 53, 62, 63, 65, 66], "like": [3, 4, 8, 9, 11, 12, 14, 18, 29, 30, 31, 32, 37, 39, 42, 50, 52, 62, 63, 65, 66], "immedi": [3, 21, 29], "clear": [3, 9, 17, 36, 57, 63, 69], "what": [3, 8, 15, 21, 22, 25, 29, 31, 39, 41, 43, 46, 47, 51, 55, 57, 59, 62, 63, 64, 66, 68], "exactli": [3, 14, 33, 34, 35, 45, 50, 51, 53, 55, 62, 63, 66], "where": [3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 35, 37, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68, 69], "come": [3, 4, 14, 15, 30, 36, 42, 50, 63], "plai": [3, 8, 36, 46, 50, 53, 63], "thei": [3, 5, 8, 16, 18, 22, 24, 29, 30, 31, 32, 36, 37, 39, 42, 49, 51, 53, 57, 62, 63, 65, 66, 68, 69], "procedur": [3, 37, 55, 63], "long": [3, 4, 14, 16, 22, 25, 29, 46, 47, 60, 63, 69], "standard": [3, 5, 6, 8, 13, 14, 22, 35, 39, 41, 42, 50, 58, 62, 69], "fashion": [3, 4, 53], "practition": [3, 49], "often": [3, 4, 16, 21, 28, 32, 35, 51, 63, 66, 69], "boil": 3, "down": [3, 17, 23, 30, 35, 47, 62, 63, 64], "pass": [3, 4, 5, 18, 20, 21, 24, 28, 42, 50, 68], "softwar": [3, 26], "regardless": [3, 4, 8, 12, 18, 29, 46, 52, 60], "wa": [3, 5, 7, 14, 25, 29, 30, 32, 35, 36, 37, 39, 45, 46, 47, 48, 49, 53, 55, 59, 63, 65], "stori": [3, 46, 47], "behind": 3, "To": [3, 5, 8, 18, 21, 22, 23, 24, 25, 27, 29, 30, 35, 37, 39, 42, 44, 45, 49, 50, 53, 55, 57, 59, 60, 62, 63, 65, 66, 68], "do": [3, 4, 8, 20, 23, 25, 29, 30, 31, 33, 35, 39, 41, 45, 53, 55, 57, 62, 63, 65, 66, 68, 69], "interfac": [3, 4, 5, 14, 45, 69], "commun": [3, 5, 7, 20, 25, 27, 64], "adopt": [3, 8, 26, 32, 42, 44, 47, 55], "python": [3, 5, 8, 13, 17, 20, 21, 25, 29, 30, 32, 37, 40, 41, 42, 45, 50, 53, 57, 66, 68, 69], "base": [3, 7, 12, 13, 19, 21, 26, 29, 32, 35, 40, 41, 42, 47, 49, 50, 51, 52, 57, 63, 65, 68, 69], "carri": [3, 24, 35], "ll": [4, 39], "revisit": [4, 16, 25, 43, 61], "time": [4, 5, 6, 8, 14, 18, 20, 23, 24, 25, 26, 27, 30, 31, 33, 35, 36, 37, 39, 40, 42, 45, 46, 49, 50, 51, 52, 53, 57, 59, 62, 63, 65, 66, 68, 69], "capabl": [4, 7, 26, 39, 55], "scale": [4, 7, 29, 30, 35, 37, 39, 42, 57, 60, 62, 63, 66], "enabl": [4, 5, 28, 29, 45, 50, 68], "vari": [4, 12, 38, 50, 52, 55, 57, 64], 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[4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 42, 44, 49, 50, 52, 55, 57, 59, 60, 63, 65, 66, 69], "test": [4, 5, 19, 21, 29, 35, 37, 42, 49, 50, 68, 69], "verifi": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 44, 46, 48, 50, 52, 53, 55, 57, 59, 60, 62, 66], "store": [4, 5, 18, 21, 22, 29, 30, 32, 35, 42, 45, 50, 52, 59, 60, 63, 65, 66, 68, 69], "sy": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "modul": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "pip": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "dev": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66], "null": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66], "highspi": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 52, 53, 59, 60, 62, 63, 64, 65, 66], "appsi_high": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 53, 55, 59, 60, 62, 63, 64, 65, 66], "environ": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "pyo": [4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "solverfactori": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "assert": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 55, 57, 60], "basic": [4, 16, 17, 21, 27, 42, 55, 65, 68, 69], "previou": [4, 5, 9, 12, 15, 18, 28, 29, 35, 42, 45, 50, 51, 63], "were": [4, 18, 27, 30, 35, 42, 49, 62, 65], "distinct": [4, 22, 29], "evid": [4, 20], "compris": [4, 21, 23, 25, 31, 37, 40, 59, 68, 69], "abbrevi": [4, 29, 68], "m": [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "factor": [4, 7, 20, 31, 42, 44, 48, 50, 55, 62, 65, 69], "attribut": [4, 5, 7, 14, 29, 35, 37, 45, 65, 68, 69], "built": [4, 20, 57], "librari": [4, 5, 8, 13, 21, 30, 32, 33, 40, 41, 44, 45, 47, 49, 50, 69], "handl": [4, 23, 26, 45, 68], "tabular": [4, 5], "sever": [4, 5, 6, 7, 11, 16, 19, 24, 26, 28, 29, 36, 37, 39, 42, 49, 57, 69], "option": [4, 5, 14, 21, 27, 29, 33, 41, 42, 50, 63, 65, 68, 69], "would": [4, 7, 8, 12, 15, 17, 18, 19, 21, 25, 26, 29, 31, 32, 33, 35, 39, 42, 45, 48, 49, 50, 52, 53, 55, 57, 59, 62, 63, 64, 65, 66, 68], "appropri": [4, 5, 42, 50], "task": [4, 16, 20, 24, 29, 30, 32, 37, 42, 53], "nest": [4, 37, 63, 68, 69], "dictionari": [4, 18, 21, 29, 34, 35, 37, 42, 45, 50, 53, 57, 63, 69], "column": [4, 5, 7, 12, 14, 15, 18, 20, 22, 24, 25, 29, 30, 31, 32, 35, 39, 42, 45, 49, 50, 52, 53, 62, 64, 66, 69], "show": [4, 5, 7, 9, 12, 13, 14, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 57, 59, 60, 62, 63, 66, 68, 69], "repres": [4, 6, 8, 18, 19, 22, 23, 25, 31, 33, 34, 35, 37, 39, 42, 44, 45, 46, 47, 49, 50, 57, 59, 68, 69], "kei": [4, 5, 8, 14, 20, 21, 29, 32, 33, 34, 35, 37, 40, 46, 49, 52, 53, 57, 59, 60, 63, 65, 66, 68, 69], "outermost": 4, "inner": [4, 42, 50], "float": [4, 30, 42, 50, 52, 60, 69], "none": [4, 5, 7, 20, 21, 27, 29, 30, 32, 34, 35, 40, 42, 45, 47, 50, 52, 57, 66, 68], "print": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68], "item": [4, 21, 30, 32, 34, 35, 37, 50, 53, 57, 59, 60, 65, 66, 69], "consum": [4, 21, 35, 57, 65, 69], "8s": [4, 29, 49], "row": [4, 5, 7, 8, 22, 29, 31, 35, 42, 53, 63, 66, 69], "label": [4, 7, 13, 15, 24, 27, 29, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 45, 50, 52, 53, 57, 60, 66, 69], "4s": 4, "By": [4, 5, 7, 14, 30, 31, 32, 55, 69], "rearrang": [4, 42], "straightforward": [4, 18, 55, 69], "becom": [4, 8, 9, 14, 19, 20, 22, 25, 29, 38, 39, 41, 42, 45, 47, 49, 50, 57, 58, 59, 60, 65, 66], "collect": [4, 5, 6, 7, 11, 13, 15, 20, 21, 27, 31, 32, 33, 35, 40, 42, 50, 62, 63, 69], "compar": [4, 7, 8, 13, 14, 19, 20, 22, 29, 30, 37, 39, 40, 42, 45, 47, 50, 59, 60, 62, 64, 66], "adapt": [4, 15, 49, 57, 62, 63, 65], "let": [4, 7, 8, 9, 11, 12, 15, 19, 20, 21, 25, 27, 29, 30, 33, 34, 35, 37, 38, 39, 44, 45, 47, 50, 52, 55, 57, 58, 59, 62, 63, 65, 68], "cal": [4, 50], "p": [4, 11, 12, 18, 23, 24, 26, 33, 35, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 53, 57, 58, 60, 62, 65, 66, 68], "respect": [4, 5, 8, 14, 18, 21, 26, 27, 29, 30, 32, 34, 35, 37, 39, 42, 46, 55, 57, 62, 63, 64, 66, 68], "x_r": [4, 39], "y_p": 4, "denot": [4, 8, 12, 15, 18, 19, 21, 23, 26, 27, 29, 30, 31, 35, 37, 39, 40, 49, 53, 57, 62, 65, 69], "constrain": [4, 12, 15, 16, 29, 35, 39, 45, 46, 49], "zero": [4, 13, 19, 29, 35, 37, 40, 41, 42, 44, 45, 50, 52, 60, 63, 65, 66], "b_r": 4, "b_p": 4, "b_q": 4, "don": [4, 8, 29, 57, 66, 69], "insert": [4, 5, 32, 45, 47], "larger": [4, 8, 20, 27, 30, 33, 37, 42, 47, 50, 53, 59], "than": [4, 5, 8, 10, 12, 15, 16, 17, 20, 21, 23, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 39, 42, 46, 47, 49, 50, 52, 53, 55, 57, 59, 60, 62, 63, 65], "ever": [4, 42, 50], "design": [4, 5, 14, 19, 22, 27, 32, 39, 40, 42, 43, 66, 68], "caus": [4, 5, 39, 68], "ignor": [4, 35, 42, 50, 57], "befor": [4, 13, 20, 21, 22, 30, 33, 39, 40, 42, 46, 53, 57, 59, 60, 62, 63, 65, 66], "sum_": [4, 7, 12, 13, 14, 15, 18, 20, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 57, 58, 59, 62, 63, 65, 66, 69], "c_p": 4, "c_r": 4, "a_": [4, 15, 25, 29, 31, 37], "put": [4, 42, 59, 63, 65], "piec": [4, 21, 37], "flexibl": [4, 32, 35, 36, 63, 68], "particular": [4, 14, 16, 21, 25, 30, 33, 35, 37, 39, 40, 45, 55, 62, 63, 65, 66, 69], "hold": [4, 5, 8, 9, 12, 14, 16, 18, 24, 27, 29, 35, 45, 52, 57, 59, 60, 62, 63, 65, 66], "scienc": [4, 5, 25, 32, 44, 45, 46, 62, 64], "see": [4, 5, 20, 21, 25, 26, 30, 31, 40, 44, 45, 46, 48, 50, 55, 57, 60, 63, 64, 65, 66, 68], "facilit": [4, 8, 14, 69], "construct": [4, 5, 7, 9, 14, 18, 21, 29, 32, 37, 38, 42, 44, 45, 50, 53, 65, 66, 68, 69], "initi": [4, 7, 8, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 46, 48, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "assign": [4, 5, 15, 16, 19, 22, 24, 25, 29, 30, 31, 32, 33, 37, 41, 42, 50, 51, 66], "decor": [4, 5, 8, 9, 25, 32, 62], "declar": [4, 5, 35, 65, 66, 69], "return": [4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68, 69], "form": [4, 6, 22, 23, 36, 44, 45, 51, 58, 60, 63, 65, 68], "param": [4, 7, 12, 14, 15, 18, 21, 22, 23, 24, 25, 27, 29, 30, 32, 39, 42, 52, 57, 60, 65, 68, 69], "omit": [4, 69], "emb": 4, "extern": [4, 21, 44, 55], "directli": [4, 5, 7, 14, 22, 23, 32, 35, 44, 45, 50, 59], "effect": [4, 5, 21, 23, 34, 44, 46, 47, 53, 68], "keep": [4, 12, 18, 25, 33, 35, 39, 50, 53, 63, 65, 69], "shorter": 4, "remov": [4, 6, 8, 15, 29, 37, 42, 53], "overhead": 4, "blur": 4, "boundari": [4, 27, 69], "statement": [4, 30, 32, 62], "edit": [4, 37, 46], "locat": [4, 16, 24, 29, 32, 34, 39, 41, 42, 57, 59, 69], "portion": [4, 49], "therebi": 4, "significantli": [4, 8, 27, 30, 39, 42, 50], "improv": [4, 5, 25, 39, 42, 44, 45, 47, 64], "maintainabi": 4, "concern": [4, 30], "overkil": 4, "small": [4, 5, 8, 12, 25, 26, 29, 30, 31, 33, 34, 37, 39, 41, 63, 65, 69], "consider": [4, 14, 15, 21, 25, 32, 42, 59, 69], "note": [4, 5, 9, 11, 12, 13, 14, 15, 17, 18, 20, 24, 25, 32, 33, 34, 35, 37, 40, 41, 42, 48, 55, 57, 60, 62, 66, 68, 69], "becaus": [4, 8, 11, 18, 21, 25, 27, 29, 30, 32, 35, 37, 39, 42, 45, 50, 53, 55, 57, 63, 65, 68, 69], "take": [4, 5, 7, 8, 9, 11, 16, 17, 18, 21, 22, 23, 24, 27, 29, 31, 33, 35, 38, 39, 42, 45, 47, 48, 50, 51, 53, 55, 57, 58, 59, 60, 62, 63, 65, 66, 68], "logic": [4, 5, 8, 12, 17, 18, 19, 22, 26, 29, 52, 55, 69], "def": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "coeffici": [4, 6, 7, 8, 13, 15, 17, 18, 29, 40, 42, 44, 50, 55, 62, 63], "cp": [4, 41], "cr": 4, "argumentn": 4, "var": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 48, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "fix": [4, 5, 6, 7, 12, 14, 24, 25, 27, 30, 32, 35, 40, 44, 45, 46, 47, 49, 57, 60, 62, 63, 64, 65, 66, 68], "done": [4, 5, 21, 22, 39, 42, 59, 63], "parlanc": 4, "sometim": [4, 36, 46, 58], "call": [4, 8, 24, 27, 29, 31, 32, 35, 38, 39, 40, 42, 48, 49, 50, 53, 59, 62, 66, 68], "rule": [4, 12, 29, 39, 45, 60, 61, 63, 65, 69], "lambda": [4, 18, 19, 20, 21, 22, 25, 27, 29, 31, 35, 39, 42, 44, 46, 47, 49, 50, 52, 53, 55, 57, 60, 65, 66, 68, 69], "argument": [4, 5, 18, 33, 39, 42, 50, 55, 62, 63, 65, 68, 69], "member": [4, 30, 32], "tupl": [4, 5, 8, 21, 25, 29, 37, 68], "quicksum": [4, 12, 18, 30, 33, 52, 55], "accept": [4, 5, 21, 22, 29, 32, 42, 46, 49, 57, 63, 69], "success": [4, 7, 47, 68, 69], "sum": [4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "sens": [4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 46, 47, 48, 49, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "Then": [4, 22, 33, 34, 35, 42, 50, 53, 55, 62, 65, 66, 68], "associ": [4, 21, 24, 26, 32, 34, 35, 37, 40, 68, 69], "manner": [4, 32], "block": [4, 25, 37, 39, 44, 45, 46, 47, 49, 50, 55, 63, 68], "materials_us": [4, 68], "report": [4, 14, 18, 29, 30, 35, 37, 39, 42, 50, 52, 55, 57, 60, 62, 68, 69], "access": [4, 21, 32, 35, 45, 57, 68], "iter": [4, 5, 18, 29, 55, 63, 68, 69], "pprint": [4, 69], "nproduct": 4, "nresourc": 4, "3": [4, 7, 11, 12, 14, 15, 18, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 58, 59, 60, 63, 66, 69], "size": [4, 5, 7, 12, 13, 14, 22, 24, 25, 27, 29, 32, 37, 38, 39, 40, 42, 45, 47, 48, 49, 50, 52, 53, 55, 57, 59, 60, 62, 69], "dimen": [4, 21, 32, 33], "a_index": 4, "true": [4, 5, 7, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 60, 62, 63, 64, 65, 66, 68, 69], "6": [4, 7, 9, 10, 12, 14, 18, 19, 20, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 41, 42, 44, 45, 46, 49, 50, 52, 53, 55, 57, 58, 59, 63, 64, 66], "5": [4, 7, 9, 10, 12, 14, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 55, 58, 63, 65, 66, 68, 69], "default": [4, 5, 8, 14, 21, 24, 25, 29, 32, 33, 39, 42, 50, 66, 69], "mutabl": [4, 14, 25, 27, 32, 57, 60, 69], "fals": [4, 5, 8, 14, 20, 21, 22, 25, 26, 30, 32, 33, 35, 37, 39, 40, 42, 45, 50, 52, 53, 55, 57, 60, 62, 63, 65, 66, 68], "stale": [4, 5, 32, 40], "activ": [4, 5, 25, 26, 29, 32, 35, 55, 66], "bodi": [4, 5, 32, 50], "inf": [4, 5, 63], "12": [4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 35, 37, 42, 45, 47, 48, 50, 53, 55, 59, 62, 63, 69], "date": [4, 5, 13, 14, 18, 25, 26, 31, 42, 49], "2023": [4, 5, 18, 20, 23, 24, 25, 26, 27, 29, 30, 31, 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9, 12, 13, 17, 22, 27, 29, 30, 33, 35, 38, 39, 40, 42, 44, 45, 47, 48, 50, 55, 57, 59, 60, 62, 63, 65, 66], "pmatrix": [8, 63], "just": [8, 11, 21, 29, 32, 34, 37, 39, 44, 55, 59, 63, 65], "rewrit": [8, 13, 17, 35, 40, 44, 45, 47, 48, 58, 63], "12x_1": [8, 10, 17, 55], "9x_2": [8, 10, 17, 55], "bmatrix": [8, 19, 22, 24, 26, 27, 42, 45, 50], "system": [8, 18, 29, 31, 35, 39, 46, 47, 56, 63, 66], "read": [8, 14, 21, 23, 29, 35, 37, 44, 49, 57, 62, 63, 66, 68, 69], "correctli": [8, 18, 25, 42, 66], "replic": 8, "4x_1": [8, 10, 55], "longleftrightarrow": [8, 44, 45], "arrai": [8, 13, 38, 40, 42, 44, 45, 48, 49, 50, 55, 57, 58, 62, 63, 65, 66, 69], "l": [8, 19, 29, 37, 39, 42, 44, 45, 46, 48, 49, 63, 69], "2x_2": [8, 10, 55], "x1": [8, 9, 10, 11, 17, 27, 44], "x2": [8, 9, 10, 11, 17, 27], "1f": [8, 10, 11, 15, 21, 42, 46, 50, 60], "650": [8, 10, 55, 59], "1100": [8, 10, 18, 29, 55], "17700": [8, 9, 10, 55], "emploi": [8, 13, 25, 42], "enhanc": [8, 27, 69], "thu": [8, 17, 18, 25, 29, 30, 33, 35, 40, 48, 57, 60, 62, 63, 66], "util": [8, 27, 29, 32, 46, 47, 49, 53, 68], "encompass": 8, "advantag": [8, 18, 28, 30, 31, 42, 50, 68], "concis": [8, 20], "space": [8, 16, 44, 45, 53, 62, 68], "clariti": 8, "reveal": [8, 39, 50], "across": [8, 29, 34, 35, 63, 65], "furthermor": [8, 18, 23, 44, 69], "unnecessari": [8, 69], "theoret": [8, 52, 60], "streamlin": [8, 21, 69], "Is": [8, 15, 30, 46], "answer": [8, 42, 59], "textit": 8, "sign": [8, 42, 50], "onc": [8, 22, 23, 37, 42, 50, 62, 66], "commit": [8, 31, 65], "deriv": [8, 22, 27, 35, 41, 42, 45, 50, 62], "sort": [8, 14, 20, 21, 25, 29, 33, 42, 46, 50], "consid": [8, 11, 13, 14, 15, 18, 20, 21, 22, 24, 27, 28, 29, 30, 31, 32, 33, 37, 38, 39, 40, 42, 44, 46, 47, 48, 49, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 68], "anywai": [8, 30, 63], "without": [8, 15, 23, 27, 32, 33, 37, 39, 42, 46, 47, 50, 53, 59, 63, 68, 69], "Of": [8, 16, 63], "cours": [8, 16, 17, 22, 33, 39, 63, 69], "illustr": [8, 12, 18, 20, 21, 26, 27, 29, 30, 37, 44, 45, 52, 55, 60, 65, 66], "shall": [8, 18, 45, 50, 65], "upon": [8, 21, 57], "had": [8, 17, 18, 29, 42, 50, 59, 65], "neg": [8, 9, 17, 18, 21, 29, 34, 35, 37, 38, 42, 45, 47, 50, 51, 57, 59, 62, 69], "therefor": [8, 14, 27, 32, 35, 38, 42, 45, 50, 62, 63, 66], "overlin": 8, "side": [8, 9, 14, 25, 29, 30, 42, 55, 57, 68], "One": [8, 9, 15, 19, 21, 22, 27, 29, 30, 35, 37, 38, 63, 65, 68], "inde": [8, 20, 25, 44, 50, 57, 63, 65], "yield": [8, 10, 17, 18, 27, 29, 39, 41, 45, 50, 52, 53, 55, 57, 63, 64, 68], "n_var": 8, "n_constraint": 8, "constraintlist": [8, 11, 60], "optimal_x": 8, "round": [8, 12, 14, 17, 18, 24, 25, 30, 31, 32, 33, 34, 37, 38, 39, 41, 44, 45, 48, 52, 55, 62, 64, 65], "addition": [8, 58, 63], "avoid": [8, 12, 18, 19, 21, 22, 27, 32, 33, 42, 52, 66, 68, 69], "hard": [8, 27, 29, 42, 50, 63], "doc": [8, 37, 45, 48, 69], "lambda_1": 9, "lambda_2": 9, "lambda_3": 9, "lambda_4": 9, "four": [9, 24, 39, 41, 42, 50, 63], "rh": [9, 50], "tight": [9, 20, 22, 24, 40, 52, 58], "Such": 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