benmoran/PuLP Simple LP Secret

## PuLP Simple LP
{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Import PuLP modeler functions\n",
      "from pulp import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = LpVariable('x', -10, 10)\n",
      "y = LpVariable('y', -10, 10)\n",
      "prob = LpProblem(\"Toy Problem\", LpMinimize)\n",
      "prob += 3*x - y\n",
      "prob.solve()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$1$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAzRAiu5mrdu/dZmiL4QAAAAAJcEhZcwAA\nDsQAAA7EAZUrDhsAAAAjSURBVAgdY2BgEGJgYDDZxMCgEgYkGNhJJVgzdmYB9TEwAACPpQrvlUCH\ncAAAAABJRU5ErkJggg==\n",
       "prompt_number": 2,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "Toy Problem:\n",
        "MINIMIZE\n",
        "3*x + -1*y + 0\n",
        "VARIABLES\n",
        "-10 <= x <= 10 Continuous\n",
        "-10 <= y <= 10 Continuous\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(x.value(), y.value())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}-10.0, & 10.0\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIIAAAAaBAMAAACJGJngAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n2T+Sv6fmmd4nJtevAAAAAElFTkSuQmCC\n",
       "prompt_number": 4,
       "text": [
        "(-10.0, 10.0)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def obj(x,y):\n",
      "    return 3*x - y\n",
      "def add_constraint(cx, cy, c):\n",
      "    # cx.x + cy.y = c\n",
      "    # x = c - cy/cx . y\n",
      "    # y = c - cx/cy . x\n",
      "    if cy != 0:\n",
      "        plot([LO, HI], [c - LO*cx/cy, c - HI*cx/cy])\n",
      "    else:\n",
      "        plot([c - LO*cy/cx, c - HI*cy/cx], [LO, HI] )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "LO = -11\n",
      "HI = 11\n",
      "xx = yy = np.linspace(LO, HI)\n",
      "XX,YY = np.meshgrid(xx,yy)\n",
      "contourf(XX,YY,obj(XX,YY), 100)\n",
      "xlim(LO, HI)\n",
      "ylim(LO, HI)\n",
      "xlabel('x')\n",
      "ylabel('y')\n",
      "add_constraint(1,0, 10)\n",
      "add_constraint(1,0, -10)\n",
      "add_constraint(0,1, -10)\n",
      "add_constraint(0,1, 10)\n",
      "plot(x.value(), y.value(), markersize=30,  marker='*')\n",
      "colorbar()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x537a488>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Js2OjzaTf0vTRYrHGxuzq6mr07Nk0YFx99dXYuXNn0N9b0QFbwdjIl1HVxNgoYmyUsPFy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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4f37c90>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob += (x+0.8*y >= 3), \"extra constraint\"\n",
      "prob += (x-0.8*y <= -3), \"c2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#prob += (x-0.8*y == 3), \"c3\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob.solve()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$1$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAzRAiu5mrdu/dZmiL4QAAAAAJcEhZcwAA\nDsQAAA7EAZUrDhsAAAAjSURBVAgdY2BgEGJgYDDZxMCgEgYkGNhJJVgzdmYB9TEwAACPpQrvlUCH\ncAAAAABJRU5ErkJggg==\n",
       "prompt_number": 10,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "XX,YY = np.meshgrid(xx,yy)\n",
      "contourf(XX,YY,obj(XX,YY), 100)\n",
      "xlim(LO, HI)\n",
      "ylim(LO, HI)\n",
      "xlabel('x')\n",
      "ylabel('y')\n",
      "add_constraint(1,0.8,3)\n",
      "add_constraint(1,-0.8,-3)\n",
      "\n",
      "add_constraint(1,0,10)\n",
      "add_constraint(1,0,-10)\n",
      "add_constraint(0,1,-10)\n",
      "add_constraint(0,1,10)\n",
      "plot(x.value(), y.value(), markersize=30,  marker='*')\n",
      "colorbar()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x58bdcf8>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Z6LF4b8B2NUI2ynC3bDRHj2nf0bDzH3zU7TWy0pzzEPrfz2cyYeVl3o9/kJbV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\n7k1UVBRxcXFcvHgRgNTUVOLi4oiKiqJ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       "text": [
        "<matplotlib.figure.Figure at 0x5369590>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prob"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "Toy Problem:\n",
        "MINIMIZE\n",
        "3*x + -1*y + 0\n",
        "SUBJECT TO\n",
        "extra_constraint: x + 0.8 y >= 3\n",
        "\n",
        "c2: x - 0.8 y <= -3\n",
        "\n",
        "VARIABLES\n",
        "-10 <= x <= 10 Continuous\n",
        "-10 <= y <= 10 Continuous\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.value(), y.value()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}-5.0, & 10.0\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAAAaBAMAAACOdoWwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n9+mx5YGctxBZ2R8+UeXb/Zls9bwlA+I5cIOGZLo/XbkAAAAASUVORK5CYII=\n",
       "prompt_number": 28,
       "text": [
        "(-5.0, 10.0)"
       ]
      }
     ],
     "prompt_number": 28
    }
   ],
   "metadata": {}
  }
 ]
}