wk-11a-Fall 2016-graphical-solution

wk-11a-Fall 2016-graphical-solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "List of constraints:\n",
    "\n",
    "4x1 + 10x2 <= 100\n",
    "\n",
    "2x1 +  1x2 <=  22\n",
    "\n",
    "3x2 +  3x2 <=  39"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# x1 >= 0\n",
    "x1 = np.linspace(0, 30, 3000)\n",
    "\n",
    "# x2 >= 0\n",
    "y1 = x1*0\n",
    "\n",
    "# 4x1 + 10x2 <= 100\n",
    "y2 = (100 - 4*x1)/10\n",
    "\n",
    "# 2x1 +  1x2 <=  22\n",
    "y3 = 22 - 2*x1\n",
    "\n",
    "# 3x1 +  3x2 <=  39\n",
    "y4 = (39-3*x1)/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa566fa4f60>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZeM5aa40xvwPmABN9rfzMM8+UfT9ixAhGjBhRj0PX0uzZnjYA99yjDtIiErJS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\nB9t7ki6LT/BsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa567054da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make plot\n",
    "plt.plot(x1, y1, label=r'$x2\\geq 0$')\n",
    "plt.plot(x1, y2, label=r'$x2\\leq (100 - 4*x1)/10$')\n",
    "plt.plot(x1, y3, label=r'$x2\\leq 20 - 2*x1$')\n",
    "plt.plot(x1, y4, label=r'$x2\\leq (39 - 3*x1)/3$')\n",
    "plt.xlim((0, 35))\n",
    "plt.ylim((0, 30))\n",
    "plt.xlabel(r'$x1$')\n",
    "plt.ylabel(r'$x2$')\n",
    "\n",
    "# Fill feasible region\n",
    "y5 = np.minimum(y2, y3)\n",
    "y6 = np.minimum(y4, y5)\n",
    "plt.fill_between(x1, y1, y6, where=y1<y6, color='pink', alpha=0.2)\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}