more typos fixed

optimization202/Modeling_Session_1/completed_exercise_set1.ipynb

@@ -102,19 +102,22 @@
     "\n",
     "> **Q8b.** \n",
     "\n",
-    "\\begin{align*}\n",
+    "\\begin{align}\n",
     "x_1 + x_2 + x_3 &= 6       \\\\\n",
     "3x_1 + 2x_2 + x_3 &\\ge 20  \\\\\n",
     "x_1, x_2, x_3, &\\ge 0\n",
-    "\\end{align*}\n",
+    "\\end{align}\n",
     "\n",
     "`Solution:`\n",
     "\n",
+    "Substitute $(1)$ into $(2)$:\n",
     "$3x_1 + 2x_2 + x_3 = 2x_1 + x_2 + (x_1 + x_2 + x_3) = 2x_1 + x_2 + 6$\n",
     "\n",
-    "Note that since $x_1$ and $x_2$ and both nonnegative, the first equation implies $x_1 \\le 6$ and $x_1 \\le 6$. \n",
+    "This simplifies $(2)$ as $2x_1 + x_2 \\ge 14$.\n",
+    "\n",
+    "Since $x_3$ is nonnegative, the first equation implies $x_1 + x_2\\le 6$, or $-x_1 - x_2 \\ge -6$.\n",
     "\n",
-    "Thus $2x_1 + x_2 + 6 \\le 18$ and cannot be 20 or more. \n",
+    "Adding the inequalities gives $x_1 \\ge 8$, which can't happen due to $(1)$. \n",
     "\n",
     "**Q9.** Translate the following into constraints using binary variables for deciding to invest in three stocks. Then determine if they are compatible as above. \n",
     "\n",

optimization202/Modeling_Session_2/completed_exercise_set2.ipynb

@@ -5,7 +5,7 @@
    "metadata": {},
    "source": [
     "# Back to the widget production problem\n",
-    "Let's go back to the Opti 101/201 classic: Widget production and distribution. Use the code below for as the base model for this problem. "
+    "Let's go back to the Opti 101/201 classic: Widget production and distribution. Use the code below as the base model for this problem."
    ]
   },
   {
@@ -15,7 +15,6 @@
    "outputs": [],
    "source": [
     "%pip install gurobipy\n",
-    "%pip install seaborn\n",
     "\n",
     "import pandas as pd\n",
     "import numpy as np\n",
@@ -244,14 +243,14 @@
    "source": [
     "Links to PWL in `gurobipy`:\n",
     "- [Model.addGenConstrPWL](https://docs.gurobi.com/projects/optimizer/en/current/reference/python/model.html#Model.addGenConstrPWL) command\n",
-    "- [Visualization of PWL](https://docs.gurobi.com/projects/optimizer/en/current/concepts/modeling/objectives.html#piecewise-linear-objectives) and how it gets put together\n",
+    "- [Visualization of PWL](https://docs.gurobi.com/projects/optimizer/en/current/concepts/modeling/objectives.html#piecewise-linear-objectives)\n",
     "\n",
     "### Scenario 1\n",
-    "Let's go back to the Opti 101/201 classic: Widget production and distribution. We have a new cost structure for transporting widgets we make. \n",
+    "We have a new cost structure for transporting widgets we make. \n",
     "- There will be a flat 0.50 increase for all transportation costs. \n",
     "- If we decide to bulk ship at least half of a production facility's max to any one distribution location, every widget over that half capacity number costs 60% of the new transportation cost. \n",
     "\n",
-    " So if the original cost is 2, the new cost of shipping from $p$ to $d$ for the first half of capacity is 2.5 (0.50 flat increase), and anything produces after that ships at 1.5. Update the model to reflect this (0.60 * 2.5). "
+    " So, if the original cost is 2, the new cost of shipping from $p$ to $d$ for the first half of capacity is 2.5 (0.50 flat increase), and anything produced after that ships at 1.5. Update the model to reflect this (0.60 * 2.5). "
    ]
   },
   {
@@ -986,7 +985,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Fill in the blanks in the code below to simulate an uncertain transportation cost from Cleveland to Indianapolis. We will use assume the cost is normally distributed with mean 2.3 and standard deviation 0.2. Generate 1000 samples. "
+    "Fill in the blanks in the code below to simulate an uncertain transportation cost from Cleveland to Indianapolis. We will assume the cost is normally distributed with mean 2.3 and standard deviation 0.2. Generate 1000 samples. "
    ]
   },
   {
@@ -1076,7 +1075,7 @@
    "source": [
     "### Individual chance constraint\n",
     "\n",
-    "Meeting widget demand in Nashville is now an extremely high priority. Historically, our data says that the demand here for the next sales period follow a [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution) that has a mean of 100 (in the original model, demand was 101). Fill in the code blanks below to make sure we meet the demand with probability 0.95."
+    "Meeting widget demand in Nashville is now an extremely high priority. Historically, our data says that the demand here for the next sales period follows a [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution) that has a mean of 100 (in the original model, demand was 101). Fill in the code blanks below to make sure we meet the demand with probability 0.95."
    ]
   },
   {
@@ -1318,7 +1317,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Create an optimization model where we decide the percentage of our budget to invest to **maximize the minimum** total estimated returns considering all scenarios. **HINT**: Define a single new auxillary variable."
+    "Create an optimization model where we decide the percentage of our budget to invest to **maximize the minimum** total estimated returns considering all scenarios. **HINT**: Define a single new auxiliary variable."
    ]
   },
   {
@@ -1441,8 +1440,8 @@
    "metadata": {},
    "source": [
     "You now decide that your investments need to be a little more diversified. Add any necessary variables and constraints that will:\n",
-    "- Make sure you invest in at least four sectors,  \n",
-    "- And any investment will need to be at least 10% of the budget."
+    "- Make sure you invest in at least four sectors.\n",
+    "- If an investment is made in a sector, then will need to be at least 10% of the budget."
    ]
   },
   {

optimization202/Modeling_Session_2/exercise_set2.ipynb

@@ -5,7 +5,7 @@
    "metadata": {},
    "source": [
     "# Back to the widget production problem\n",
-    "Let's go back to the Opti 101/201 classic: Widget production and distribution. Use the code below for as the base model for this problem. "
+    "Let's go back to the Opti 101/201 classic: Widget production and distribution. Use the code below as the base model for this problem."
    ]
   },
   {
@@ -15,7 +15,6 @@
    "outputs": [],
    "source": [
     "%pip install gurobipy\n",
-    "%pip install seaborn\n",
     "\n",
     "import pandas as pd\n",
     "import numpy as np\n",
@@ -137,14 +136,14 @@
    "source": [
     "Links to PWL in `gurobipy`:\n",
     "- [Model.addGenConstrPWL](https://docs.gurobi.com/projects/optimizer/en/current/reference/python/model.html#Model.addGenConstrPWL) command\n",
-    "- [Visualization of PWL](https://docs.gurobi.com/projects/optimizer/en/current/concepts/modeling/objectives.html#piecewise-linear-objectives) and how it gets put together\n",
+    "- [Visualization of PWL](https://docs.gurobi.com/projects/optimizer/en/current/concepts/modeling/objectives.html#piecewise-linear-objectives)\n",
     "\n",
     "### Scenario 1\n",
-    "Let's go back to the Opti 101/201 classic: Widget production and distribution. We have a new cost structure for transporting widgets we make. \n",
+    "We have a new cost structure for transporting widgets we make. \n",
     "- There will be a flat 0.50 increase for all transportation costs. \n",
     "- If we decide to bulk ship at least half of a production facility's max to any one distribution location, every widget over that half capacity number costs 60% of the new transportation cost. \n",
     "\n",
-    " So if the original cost is 2, the new cost of shipping from $p$ to $d$ for the first half of capacity is 2.5 (0.50 flat increase), and anything produces after that ships at 1.5. Update the model to reflect this (0.60 * 2.5). "
+    " So, if the original cost is 2, the new cost of shipping from $p$ to $d$ for the first half of capacity is 2.5 (0.50 flat increase), and anything produced after that ships at 1.5. Update the model to reflect this (0.60 * 2.5). "
    ]
   },
   {
@@ -305,7 +304,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Fill in the blanks in the code below to simulate an uncertain transportation cost from Cleveland to Indianapolis. We will use assume the cost is normally distributed with mean 2.3 and standard deviation 0.2. Generate 1000 samples. "
+    "Fill in the blanks in the code below to simulate an uncertain transportation cost from Cleveland to Indianapolis. We will assume the cost is normally distributed with mean 2.3 and standard deviation 0.2. Generate 1000 samples. "
    ]
   },
   {
@@ -384,7 +383,7 @@
    "source": [
     "### Individual chance constraint\n",
     "\n",
-    "Meeting widget demand in Nashville is now an extremely high priority. Historically, our data says that the demand here for the next sales period follow a [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution) that has a mean of 100 (in the original model, demand was 101). Fill in the code blanks below to make sure we meet the demand with probability 0.95."
+    "Meeting widget demand in Nashville is now an extremely high priority. Historically, our data says that the demand here for the next sales period follows a [Poisson distribution](https://en.wikipedia.org/wiki/Poisson_distribution) that has a mean of 100 (in the original model, demand was 101). Fill in the code blanks below to make sure we meet the demand with probability 0.95."
    ]
   },
   {
@@ -484,7 +483,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Create an optimization model where we decide the percentage of our budget to invest to **maximize the minimum** total estimated returns considering all scenarios. **HINT**: Define a single new auxillary variable."
+    "Create an optimization model where we decide the percentage of our budget to invest to **maximize the minimum** total estimated returns considering all scenarios. **HINT**: Define a single new auxiliary variable."
    ]
   },
   {
@@ -525,8 +524,8 @@
    "metadata": {},
    "source": [
     "You now decide that your investments need to be a little more diversified. Add any necessary variables and constraints that will:\n",
-    "- Make sure you invest in at least four sectors,  \n",
-    "- And any investment will need to be at least 10% of the budget."
+    "- Make sure you invest in at least four sectors.\n",
+    "- If an investment is made in a sector, then will need to be at least 10% of the budget."
    ]
   },
   {