example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5397acb-dfa2-443a-a655-d3012051839c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sympy import Symbol, solve"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2478077-bf0d-4898-bd9f-e35baa6727ab",
   "metadata": {},
   "source": [
    "## The Problem\n",
    "<div>\n",
    "    <table>\n",
    "        <thead>\n",
    "            <tr>\n",
    "                <th>Machine</th>\n",
    "                <th>Product 1</th>\n",
    "                <th>Product 2</th>\n",
    "                <th>Available Hours</th>\n",
    "            </tr>\n",
    "        </thead>\n",
    "        <tbody>\n",
    "            <tr>\n",
    "                <td>Machine 1</td>\n",
    "                <td>2 hrs</td>\n",
    "                <td>1 hr</td>\n",
    "                <td>8 hrs</td>\n",
    "            </tr>\n",
    "            <tr>\n",
    "                <td>Machine 2</td>\n",
    "                <td>1 hr</td>\n",
    "                <td>2 hrs</td>\n",
    "                <td>8 hrs</td>\n",
    "            </tr>\n",
    "        </tbody>\n",
    "        <tfoot>\n",
    "            <tr>\n",
    "                <td>Unit Profit</td>\n",
    "                <td>&#36;300</td>\n",
    "                <td>&#36;200</td>\n",
    "                <td>&nbsp;</td>\n",
    "            </tr>\n",
    "        </tfoot>\n",
    "    </table>\n",
    "</div>\n",
    "<div>\n",
    "    <div>Maximize Profit: Z = &#36;300x<sub>1</sub> + &#36;200x<sub>2</sub></div>\n",
    "    <div>Subject to:</div>\n",
    "    <div>2x<sub>1</sub> + 1x<sub>2</sub> <= 8</div>\n",
    "    <div>1x<sub>1</sub> + 2x<sub>2</sub> <= 8</div>\n",
    "    <div>x<sub>1</sub> >= 0, x<sub>2</sub> >= 0</div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "96d18e25-110d-4ecd-9f22-9ababce88d25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b1_x1 = 2; b1_x2 = 1; lim1 = 8\n",
    "b2_x1 = 1; b2_x2 = 2; lim2 = 8\n",
    "m1_profit = 300\n",
    "m2_profit = 200\n",
    "\n",
    "def get_bound(x1, x2, constraint):\n",
    "    x_1 = [constraint/x1, 0.0]\n",
    "    x_2 = [0.0, constraint/x2]\n",
    "    return x_1, x_2\n",
    "\n",
    "\n",
    "def plot_solution(b1_x1, b1_x2, lim1, b2_x1, b2_x2, lim2):\n",
    "    s1 = Symbol('x1')\n",
    "    s2 = Symbol('x2')\n",
    "\n",
    "    x1, y1 = get_bound(b1_x1, b1_x2, lim1)\n",
    "    x2, y2 = get_bound(b2_x1, b2_x2, lim2)\n",
    "    \n",
    "    x1_exp = (lim2 - (b2_x2*s2)) / b2_x1\n",
    "    x2_exp = b1_x1*(x1_exp) + b1_x2*s2 - lim1\n",
    "\n",
    "    constraint1 = b1_x1*s1 + b1_x2*s2 - lim1\n",
    "    constraint2 = b2_x1*s1 + b2_x2*s2 - lim2\n",
    "    soln = solve((constraint1, constraint2), dict=True)[0]\n",
    "    \n",
    "    intersect_x = soln[s1]\n",
    "    intersect_y = soln[s2]\n",
    "    max_profit = m1_profit*s1 + m2_profit*s2\n",
    "    max_profit = float(max_profit.subs({'x1': intersect_x, 'x2': intersect_y}))\n",
    "\n",
    "    plt.plot(x1, y1, linestyle=':', marker='o', color='green')\n",
    "    plt.plot(x2, y2, linestyle=':', marker='o', color='blue')\n",
    "    plt.plot(intersect_x, intersect_y, marker='o', color='red')\n",
    "    plt.plot(0,0, marker='o')\n",
    "    plt.plot([0, 0], [lim1, 0], linestyle=':', color='gray')\n",
    "    plt.plot([lim2, 0], [0, 0], linestyle=':', color='gray')\n",
    "    plt.fill(\n",
    "        [0, 0, intersect_x, x1[0]],\n",
    "        [0, y2[1], intersect_y, 0],\n",
    "        color='pink', alpha=0.5\n",
    "    )\n",
    "    plt.annotate(\n",
    "        f\"Optimal: ({intersect_x}, {intersect_y})\\nMax Profit: ${max_profit:0.2f}\", # this is the text\n",
    "        (intersect_x, intersect_y), # these are the coordinates to position the label\n",
    "        textcoords=\"offset points\", # how to position the text\n",
    "        xytext=(4,4), # distance from text to points (x,y)\n",
    "        ha='left') # horizontal alignment can be left, right or center\n",
    "\n",
    "    plt.annotate(\n",
    "        \"Feasible Region\", # this is the text\n",
    "        (intersect_x, intersect_y), # these are the coordinates to position the label\n",
    "        textcoords=\"offset points\", # how to position the text\n",
    "        xytext=(0,-20), # distance from text to points (x,y)\n",
    "        ha='right') # horizontal alignment can be left, right or center\n",
    "\n",
    "    plt.annotate(\n",
    "        f\"Constraint: {constraint1}\", # this is the text\n",
    "        (0, lim1), # these are the coordinates to position the label\n",
    "        textcoords=\"offset points\", # how to position the text\n",
    "        xytext=(12,-8), # distance from text to points (x,y)\n",
    "        ha='left') # horizontal alignment can be left, right or center\n",
    "\n",
    "    plt.annotate(\n",
    "        f\"Constraint: {constraint2}\", # this is the text\n",
    "        (lim2, 0), # these are the coordinates to position the label\n",
    "        textcoords=\"offset points\", # how to position the text\n",
    "        xytext=(-0,12), # distance from text to points (x,y)\n",
    "        ha='right') # horizontal alignment can be left, right or center\n",
    "    \n",
    "    plt.show()\n",
    "\n",
    "\n",
    "plot_solution(b1_x1, b1_x2, lim1, b2_x1, b2_x2, lim2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eea9c47a-b272-43a2-ab9d-deff30580a74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d1ed2638995848efa7797ccbb0b62db8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=2, description='b1_x1', max=6, min=-2), IntSlider(value=1, description='…"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import ipywidgets as widgets\n",
    "\n",
    "b1_x1_slider = widgets.IntSlider(value=b1_x1, min=1, max=10, step=1, description='b1_x1')\n",
    "b1_x2_slider = widgets.IntSlider(value=b1_x2, min=1, max=10, step=1, description='b1_x2')\n",
    "lim1_slider = widgets.IntSlider(value=lim1, min=1, max=10, step=1, description='Max Hrs Machine 1')\n",
    "\n",
    "b2_x1_slider = widgets.IntSlider(value=b2_x1, min=1, max=10, step=1, description='b2_x1')\n",
    "b2_x2_slider = widgets.IntSlider(value=b2_x2, min=1, max=10, step=1, description='b2_x2')\n",
    "lim2_slider = widgets.IntSlider(value=lim2, min=1, max=10, step=1, description='Max Hrs Machine 2')\n",
    "\n",
    "def compute(b1_x1, b1_x2, lim1, b2_x1, b2_x2, lim2):\n",
    "    try:\n",
    "        plot_solution(b1_x1,b1_x2,lim1,b2_x1,b2_x2,lim2)\n",
    "    except:\n",
    "        pass\n",
    "\n",
    "widgets.interactive(\n",
    "    compute,\n",
    "    b1_x1=b1_x1_slider.value,\n",
    "    b1_x2=b1_x2_slider.value,\n",
    "    lim1=lim1_slider.value,\n",
    "    b2_x1=b2_x1_slider.value,\n",
    "    b2_x2=b2_x2_slider.value,\n",
    "    lim2=lim2_slider.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa735ae5-895b-4105-b1bc-f38310528930",
   "metadata": {},
   "outputs": [],
   "source": [
    "# (0,0), (0, 4), (10/3, 7/3), (4.5, 0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
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