diff --git a/_sources/notebooks/05/markowitz_portfolio.ipynb b/_sources/notebooks/05/markowitz_portfolio.ipynb
index e1bd9d92..d8a9b328 100644
--- a/_sources/notebooks/05/markowitz_portfolio.ipynb
+++ b/_sources/notebooks/05/markowitz_portfolio.ipynb
@@ -149,7 +149,7 @@
    "id": "5f6de49c",
    "metadata": {},
    "source": [
-    "We now calculate the optimal investment strategy for a portfolio with $n=3$ assets, with expected returns $\\mu = (1.2, 1.1, 1.3)$ and a predefined covariance matrix. We set the risk parameter $\\gamma$ to $q$ and the risk-free return rate $R$ to $1.01$."
+    "We now calculate the optimal investment strategy for a portfolio with $n=3$ assets, with expected returns $\\mu = (1.2, 1.1, 1.3)$ and a predefined covariance matrix. We set the risk parameter $\\gamma$ to $1$ and the risk-free return rate $R$ to $1.01$."
    ]
   },
   {
diff --git a/notebooks/05/markowitz_portfolio.html b/notebooks/05/markowitz_portfolio.html
index f40146fe..c9f1ed85 100644
--- a/notebooks/05/markowitz_portfolio.html
+++ b/notebooks/05/markowitz_portfolio.html
@@ -607,7 +607,7 @@ <h2>Problem description and model formulation<a class="headerlink" href="#proble
 </div>
 </div>
 </div>
-<p>We now calculate the optimal investment strategy for a portfolio with <span class="math notranslate nohighlight">\(n=3\)</span> assets, with expected returns <span class="math notranslate nohighlight">\(\mu = (1.2, 1.1, 1.3)\)</span> and a predefined covariance matrix. We set the risk parameter <span class="math notranslate nohighlight">\(\gamma\)</span> to <span class="math notranslate nohighlight">\(q\)</span> and the risk-free return rate <span class="math notranslate nohighlight">\(R\)</span> to <span class="math notranslate nohighlight">\(1.01\)</span>.</p>
+<p>We now calculate the optimal investment strategy for a portfolio with <span class="math notranslate nohighlight">\(n=3\)</span> assets, with expected returns <span class="math notranslate nohighlight">\(\mu = (1.2, 1.1, 1.3)\)</span> and a predefined covariance matrix. We set the risk parameter <span class="math notranslate nohighlight">\(\gamma\)</span> to <span class="math notranslate nohighlight">\(1\)</span> and the risk-free return rate <span class="math notranslate nohighlight">\(R\)</span> to <span class="math notranslate nohighlight">\(1.01\)</span>.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Specify the initial capital, the risk threshold, and the guaranteed return rate.</span>
diff --git a/searchindex.js b/searchindex.js
index 9aa9e916..d8b442f5 100644
--- a/searchindex.js
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29, 35, 55, 59, 63, 66, 68], "your": [1, 20, 23, 46, 62, 64], "journei": [1, 29], "first": [1, 2, 4, 5, 6, 8, 9, 10, 12, 14, 15, 18, 21, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 42, 44, 45, 48, 50, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68], "chapter": [1, 2, 5, 6, 15, 16, 18, 20, 22, 28, 36, 40, 43, 46, 48, 51, 53, 54, 56, 61, 63, 65, 66], "we": [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, 37, 38, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69], "seek": [1, 2, 9, 42, 50, 62, 66], "feedback": [1, 69], "If": [1, 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, 38, 39, 42, 44, 45, 46, 47, 48, 50, 52, 55, 57, 58, 60, 62, 63, 65, 66, 68, 69], "you": [1, 4, 8, 15, 20, 23, 27, 29, 35, 45, 48, 50, 55, 57, 58, 63, 64, 66, 69], "encount": [1, 4, 15, 58], "issu": [1, 14, 19, 21, 27, 29, 30, 37, 44, 63, 65], "have": [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, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 57, 59, 60, 62, 63, 64, 65, 66, 68, 69], "suggest": [1, 7, 25, 37, 49, 59, 69], "how": [1, 2, 3, 4, 8, 13, 17, 18, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 37, 38, 39, 41, 42, 44, 45, 47, 49, 50, 51, 55, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68], "better": [1, 27, 28, 29, 30, 32, 39, 42, 48, 51, 53, 63, 66, 69], "pleas": [1, 50, 65], "link": [1, 27, 29, 31, 39, 45, 53], "everi": [1, 2, 4, 5, 13, 14, 20, 21, 27, 29, 33, 34, 35, 37, 39, 47, 55, 57, 62, 63, 65, 66, 68], "github": [1, 20, 25], "cat": [1, 14, 49], "group": [1, 6, 8, 25, 32, 52, 57], "research": [1, 21, 27, 29, 37, 39, 45, 63], "educ": 1, "who": [1, 4, 14, 25, 30, 32, 37], "came": 1, "togeth": [1, 4, 18, 27, 42, 57, 59, 63, 65, 68, 69], "common": [1, 2, 4, 5, 8, 15, 20, 21, 22, 27, 29, 31, 32, 37, 39, 42, 45, 50, 62, 68, 69], "purpos": [1, 4, 21, 22, 35, 42, 45, 57, 62, 63, 65, 68], "materi": [1, 3, 4, 5, 6, 8, 16, 17, 18, 26, 28, 29, 36, 39, 43, 44, 52, 63, 69], "our": [1, 2, 8, 12, 18, 21, 22, 25, 26, 29, 30, 31, 35, 36, 42, 44, 50, 51, 53, 55, 57, 58, 59, 63, 65, 66], "classroom": 1, "teach": [1, 64, 69], "hopefulli": [1, 39, 63], "find": [1, 2, 3, 7, 9, 13, 14, 15, 20, 22, 23, 24, 27, 28, 30, 31, 32, 33, 34, 37, 39, 42, 44, 46, 49, 53, 55, 57, 59, 60, 63, 64, 65, 68], "other": [1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 39, 41, 42, 44, 45, 46, 47, 49, 50, 55, 59, 62, 63, 66, 68, 69], "most": [1, 5, 6, 9, 15, 19, 21, 22, 23, 27, 29, 31, 32, 34, 35, 37, 39, 42, 47, 49, 53, 55, 57, 60, 63, 69], "importantli": [1, 57, 65], "those": [1, 3, 4, 8, 11, 12, 21, 27, 29, 34, 42, 50, 60, 62, 63, 65], "entri": [1, 31, 39, 42, 50, 62, 69], "world": [1, 2, 31, 36, 39, 46, 49, 51, 62], "data": [1, 3, 5, 12, 16, 20, 21, 24, 26, 27, 29, 30, 34, 39, 51, 52, 55, 59, 60, 63, 68], "rich": 1, "applic": [1, 2, 4, 5, 7, 22, 25, 26, 27, 29, 31, 32, 37, 39, 42, 44, 45, 49, 50, 53, 57, 63, 65, 68, 69], "krzysztof": 1, "postek": 1, "boston": 1, "consult": [1, 45, 64], "formerli": 1, "tu": 1, "delft": 1, "alessandro": 1, "zocca": 1, "vu": 1, "amsterdam": [1, 62], "joaquim": 1, "gromicho": 1, "ortec": 1, "jeffrei": 1, "kantor": 1, "notr": 1, "dame": 1, "wish": [1, 4, 14, 21, 39, 42, 62], "cite": [1, 29, 39, 45, 49], "work": [1, 5, 6, 8, 11, 20, 22, 25, 29, 30, 31, 37, 39, 42, 45, 46, 47, 49, 50, 57, 65, 68, 69], "postekzocca2024": 1, "titl": [1, 5, 14, 20, 22, 35, 37, 42, 46, 49, 50, 53, 62, 68], "author": 1, "year": [1, 12, 18, 45, 49, 52, 64, 69], "onlin": [1, 29, 39, 66], "url": [1, 37], "http": [1, 7, 20, 29, 31, 35, 37, 39, 42, 44, 45, 46, 47, 48, 49, 50, 57, 64, 65, 66, 68], "mobook": [1, 29, 35, 42, 50, 57, 65, 66], "io": [1, 12, 18, 20, 31, 52], "mo": [1, 29, 35, 42, 50, 57, 65, 66], "broad": 2, "term": [2, 3, 4, 13, 17, 18, 20, 21, 25, 26, 29, 31, 32, 33, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 57, 59, 60, 63, 65, 66], "describ": [2, 3, 4, 6, 8, 12, 18, 21, 22, 23, 24, 25, 27, 29, 32, 34, 35, 37, 38, 41, 42, 44, 45, 48, 49, 57, 58, 59, 62, 66, 69], "wai": [2, 3, 4, 5, 8, 11, 13, 16, 20, 21, 22, 23, 28, 29, 30, 31, 32, 34, 35, 38, 39, 45, 46, 48, 49, 50, 53, 57, 58, 63, 65, 66, 68, 69], "them": [2, 4, 5, 8, 9, 16, 18, 24, 29, 30, 36, 38, 39, 49, 53, 55, 58, 62, 63, 65, 66], "us": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 59, 61, 64, 65, 66, 67], "dedic": [2, 55], "algorithm": [2, 3, 27, 29, 33, 45, 53, 63], "consist": [2, 5, 7, 13, 14, 20, 21, 25, 29, 31, 33, 35, 40, 42, 49, 50, 62, 68, 69], "three": [2, 4, 18, 21, 22, 25, 27, 31, 39, 49, 51, 59, 60, 62, 64, 68], "part": [2, 3, 21, 37, 42, 45, 50, 55, 63, 64, 65], "correspond": [2, 3, 4, 8, 9, 11, 12, 13, 14, 17, 18, 19, 22, 23, 25, 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, 38, 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, 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], 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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, 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29, 31, 32, 33, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 53, 57, 59, 60, 63, 65, 66], "describ": [2, 3, 4, 6, 8, 12, 18, 21, 22, 23, 24, 25, 27, 29, 32, 34, 35, 37, 38, 41, 42, 44, 45, 48, 49, 57, 58, 59, 62, 66, 69], "wai": [2, 3, 4, 5, 8, 11, 13, 16, 20, 21, 22, 23, 28, 29, 30, 31, 32, 34, 35, 38, 39, 45, 46, 48, 49, 50, 53, 57, 58, 63, 65, 66, 68, 69], "them": [2, 4, 5, 8, 9, 16, 18, 24, 29, 30, 36, 38, 39, 49, 53, 55, 58, 62, 63, 65, 66], "us": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 57, 59, 61, 64, 65, 66, 67], "dedic": [2, 55], "algorithm": [2, 3, 27, 29, 33, 45, 53, 63], "consist": [2, 5, 7, 13, 14, 20, 21, 25, 29, 31, 33, 35, 40, 42, 49, 50, 62, 68, 69], "three": [2, 4, 18, 21, 22, 25, 27, 31, 39, 49, 51, 59, 60, 62, 64, 68], "part": [2, 3, 21, 37, 42, 45, 50, 55, 63, 64, 65], "correspond": [2, 3, 4, 8, 9, 11, 12, 13, 14, 17, 18, 19, 22, 23, 25, 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": 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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, 38, 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, 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, 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