{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Make sure you run this at the begining**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(suppress=True)\n",
    "from scipy.optimize import linprog"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feasible Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\max f=4x_1+x_2 \\\\\n",
    "\\text{s.t.} -x_1 + 2x_2 &\\leq 4 \\\\\n",
    "2x_1 + 3x_2 &\\leq 12 \\\\\n",
    "x_1 - x_2 &\\leq 3 \\\\\n",
    "\\text{and } x_1, x_2 \\geq 0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [-4, -1, 0, 0, 0]\n",
    "A = [[-1, 2, 0, 0, 0], [2, 3, 0, 0, 0], [1, -1, 0, 0, 0]]\n",
    "b = [4, 12, 3]\n",
    "\n",
    "x0_bounds = (0, None)\n",
    "x1_bounds = (0, None)\n",
    "x2_bounds = (None, None)\n",
    "x3_bounds = (None, None)\n",
    "x4_bounds = (None, None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     con: array([], dtype=float64)\n",
      "     fun: -17.999999976555795\n",
      " message: 'Optimization terminated successfully.'\n",
      "     nit: 4\n",
      "   slack: array([5.8       , 0.00000002, 0.        ])\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([4.19999999, 1.2       , 0.        , 0.        , 0.        ])\n"
     ]
    }
   ],
   "source": [
    "res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds, x2_bounds, x3_bounds, x4_bounds])\n",
    "\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Infeasible Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\min f = x_1 - 2x_2 + 3x_3 \\\\\n",
    "s.t. -2x_1 + x_2 + 3x_3 & = 2 \\\\\n",
    "3x_1 + 3x_2 + 4x_3 & = 1 \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [-1, 2, -3]\n",
    "A = [[-2, 1, 3], [3, 3, 4]]\n",
    "b = [2, 1]\n",
    "\n",
    "x0_bounds = (0, None)\n",
    "x1_bounds = (0, None)\n",
    "x2_bounds = (0, None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     con: array([ 0.        , -4.56053464])\n",
      "     fun: -0.6099904044751114\n",
      " message: 'The algorithm terminated successfully and determined that the problem is infeasible.'\n",
      "     nit: 4\n",
      "   slack: array([], dtype=float64)\n",
      "  status: 2\n",
      " success: False\n",
      "       x: array([0.2893146 , 0.75265113, 0.60865936])\n"
     ]
    }
   ],
   "source": [
    "res = linprog(c, A_eq=A, b_eq=b, bounds=[x0_bounds, x1_bounds, x2_bounds,])\n",
    "\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1><font color='red'>Assignment</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "\\min f = 3x_1 - x_2 \\\\\n",
    "s.t. 2x_1 + x_2 & \\geq 2 \\\\\n",
    "x_1 + 3x_2 &  \\leq 3 \\\\\n",
    "x_2 &  \\leq 4 \\\\\n",
    "\\text{and } x_1, x_2 \\geq 0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [-3, 1]\n",
    "A = [[-2, -1], [1, 3], [0, 1]]\n",
    "b = [-2, 3, 4]\n",
    "\n",
    "x0_bounds = (0, None)\n",
    "x1_bounds = (0, None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     con: array([], dtype=float64)\n",
      "     fun: -8.999999998556428\n",
      " message: 'Optimization terminated successfully.'\n",
      "     nit: 4\n",
      "   slack: array([4., 0., 4.])\n",
      "  status: 0\n",
      " success: True\n",
      "       x: array([3., 0.])\n"
     ]
    }
   ],
   "source": [
    "res = linprog(c, A_ub=A, b_ub=b, bounds=[x0_bounds, x1_bounds])\n",
    "\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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