More on LP Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MSDS 400 More on LP Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot \n",
    "from matplotlib.pyplot import *\n",
    "import numpy \n",
    "from numpy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Max Z = 6X+5Y\n",
    "\n",
    "X+Y ≤ 5\n",
    "\n",
    "3X+2Y ≤ 12\n",
    "\n",
    "X ≥ 0  &  Y ≥ 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a minimization problem. One objective is to demonstrate plotting an unbounded region. There are four inequalities: \n",
    "\n",
    "x + 3y ≥ 15<br>\n",
    "3x+y ≥ 10<br>\n",
    "x >= 0, y >= 0. \n",
    "\n",
    "The objective function is z = 2x + 3y. The feasible region will be graphed and filled. Matrix methods will be used to evaluate the objective function at each corner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x= arange(0,20.1,0.1)\n",
    "y0= arange(0,20.1,0.1)\n",
    "y1= 5.0-x\n",
    "y2= 6.0-3.0*x/2.0\n",
    "y3 = 0+0.0*x  # The definition of y3 will allow filling the unbounded region in the plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The filling will be between y3 and the maximum of y1 and y2.  Need to define \n",
    "a new array y4 which will be that maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "y4 = list()  # Start as an empty list and add the greater of y1/y2 to it for each point\n",
    "for y1_val, y2_val in zip(y1, y2):\n",
    "    # Zip allows us to loop over both lists at the same time.\n",
    "    y4_val = min([y1_val, y2_val])  # Get the greater of the two\n",
    "    y4.append(y4_val)  # Add it to our list\n",
    "    \n",
    "#y5= 5.5-2.0*x/3.0  # This is the objective function plotted for illustration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlim(0,20)\n",
    "ylim(0,20)\n",
    "xlabel('x-axis')\n",
    "ylabel('y-axis')\n",
    "title('Shaded Area Shows the Feasible Region')\n",
    "plot(x,y2,color='b', label='3x+2y >= 12')\n",
    "plot(x,y1,color='r', label='x+y >= 5')\n",
    "#plot(x,y5,'k--', label='16.5 = 2x+3y')\n",
    "legend()\n",
    "fill_between(x,y3,y4, color='grey',alpha=0.2)\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Corner points for evaluation using the objective function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x= [0, 4, 2]\n",
    "y= [5, 0, 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This next step shows how to use matrix calculations to evaluate\n",
    "the objective function at each corner point and find the maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Objective Function at Each Corner Point\n",
      " [[25.]\n",
      " [24.]\n",
      " [27.]]\n"
     ]
    }
   ],
   "source": [
    "obj= matrix([6.0,5.0])\n",
    "obj= transpose(obj)\n",
    "corners= matrix([x,y])\n",
    "corners= transpose(corners)\n",
    "result= dot(corners,obj)\n",
    "print ('Value of Objective Function at Each Corner Point\\n', result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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