Practice-Task.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot \n",
    "from matplotlib.pyplot import *\n",
    "import numpy\n",
    "from numpy import arange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAe4ZqmefhfR06NrVJav58/2OzpiKwxKUMfmoVg2uucYlqEceccnpuOPc5b8l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\n5Al1KRkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5fdab34160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " calculating for point: A = 200.000000 and B = 170.000000\n",
      "solution for z =  450000.0\n",
      "\n",
      " calculating for point: A = 100.000000 and B = 170.000000\n",
      "solution for z =  650000.0\n",
      "\n",
      " calculating for point: A = 100.000000 and B = 100.000000\n",
      "solution for z =  300000.0\n",
      "\n",
      " calculating for point: A = 120.000000 and B = 80.000000\n",
      "solution for z =  160000.0\n",
      "\n",
      " calculating for point: A = 200.000000 and B = 80.000000\n",
      "solution for z =  0.0\n",
      "\n",
      " the maximum profit z = $650000.000000 @ A = 100.000000 and B = 170.000000\n"
     ]
    }
   ],
   "source": [
    "figure()\n",
    "A = arange(-100, 220, 10)\n",
    "B = arange(-100, 220, 10)\n",
    "\n",
    "# constraint equation\n",
    "\n",
    "B1 = 200.0 - A\n",
    "\n",
    "\n",
    "\n",
    "xlim = (-100, 220)\n",
    "ylim= (-100, 220)\n",
    "hlines(0, -100, 220, color = 'k')\n",
    "vlines(0, -100, 220, color = 'k')\n",
    "grid(True)\n",
    "\n",
    "xlabel('X-axis')\n",
    "ylabel('Y-axis')\n",
    "\n",
    "plot(A, B1, color = 'b')\n",
    "axhline(y = 80, color = 'r')\n",
    "axhline(y = 170, color = 'm')\n",
    "axvline(x = 200, color = 'b')\n",
    "axvline(x = 100, color = 'g')\n",
    "\n",
    "title('objective function: z = 5000B - 2000A with following constarints')\n",
    "legend(['A+B>=200','200>=A>=100','170>=B>=80'])\n",
    "\n",
    "A = [200.0,100.0, 100.0, 120.0,200.0]\n",
    "B = [170.0, 170.0, 100.0, 80.0, 80.0]\n",
    "fill(A,B,'g+')\n",
    "\n",
    "\n",
    "show()\n",
    "\n",
    "checker = 0\n",
    "for i,j in zip(A,B):\n",
    "    print('\\n calculating for point: A = {0:f} and B = {1:f}' .format(i,j))\n",
    "    print('solution for z = ', 5000*j-2000*i)\n",
    "    if(checker <= (5000*j-2000*i)):\n",
    "       checker = (5000*j-2000*i)\n",
    "       X,Y = i,j\n",
    "       \n",
    "print('\\n the maximum profit z = ${0:f} @ A = {1:f} and B = {2:f}' .format(checker,X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pulp import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.0\n",
      "60.0\n"
     ]
    }
   ],
   "source": [
    "# declare your variables\n",
    "x1 = LpVariable(\"x1\", 0, 40)   # 0<= x1 <= 40\n",
    "x2 = LpVariable(\"x2\", 0, 1000) # 0<= x2 <= 1000\n",
    " \n",
    "# defines the problem\n",
    "prob = LpProblem(\"problem\", LpMaximize)\n",
    " \n",
    "# defines the constraints\n",
    "prob += 2*x1+x2 <= 100 \n",
    "prob += x1+x2 <= 80\n",
    "prob += x1<=40\n",
    "prob += x1>=0\n",
    "prob += x2>=0\n",
    " \n",
    "# defines the objective function to maximize\n",
    "prob += 3*x1+2*x2\n",
    " \n",
    "# solve the problem\n",
    "status = prob.solve()\n",
    "LpStatus[status]\n",
    " \n",
    "# print the results x1 = 20, x2 = 60\n",
    "print(value(x1))\n",
    "print(value(x2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "printing status of the LP problem:  Optimal\n",
      "Value of model A car:  100.0\n",
      "Value of model B car:  170.0\n",
      "the optimal solution or say maximum profit: $ 650000.0\n"
     ]
    }
   ],
   "source": [
    "# declare your variables\n",
    "A = LpVariable(\"A\", 100, 200)   # 100 <= A <= 200\n",
    "B = LpVariable(\"B\", 80, 170) # 80 <= B <= 170\n",
    " \n",
    "# defines the problem\n",
    "prob = LpProblem(\"problem\", LpMaximize)\n",
    " \n",
    "# defines the constraints\n",
    "prob += A + B >=200 \n",
    "prob += A<=200\n",
    "prob += A>=100\n",
    "prob += B>=80\n",
    "prob += B<=170\n",
    " \n",
    "# defines the objective function to maximize\n",
    "prob += 5000*B-2000*A\n",
    " \n",
    "# solve the problem\n",
    "status = prob.solve()\n",
    "print('printing status of the LP problem: ', LpStatus[status])\n",
    " \n",
    "# print the results A = 100, B = 170\n",
    "print('Value of model A car: ', value(A))\n",
    "print('Value of model B car: ', value(B))\n",
    "print('the optimal solution or say maximum profit: $', value(prob.objective))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Positive directional derivative for linesearch    (Exit mode 8)\n",
      "            Current function value: -650000.0\n",
      "            Iterations: 7\n",
      "            Function evaluations: 12\n",
      "            Gradient evaluations: 3\n",
      "About solution from Optimize.minnimize: \n",
      "      fun: -650000.0\n",
      "     jac: array([ 2000., -5000.])\n",
      " message: 'Positive directional derivative for linesearch'\n",
      "    nfev: 12\n",
      "     nit: 7\n",
      "    njev: 3\n",
      "  status: 8\n",
      " success: False\n",
      "       x: array([ 100.,  170.])\n",
      "\n",
      "\n",
      "\n",
      "Printing the Results: \n",
      "\n",
      "\n",
      "\n",
      "maximum Profit Gained: $ 650000.0\n",
      "\n",
      " Number of Model A Cars:  100.0\n",
      "\n",
      " Number of Model B Cars:  170.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "#defining our Objective function\n",
    "def objective(x):\n",
    "    A = x[0]\n",
    "    B = x[1]\n",
    "    #since we are finding Max result using Minimizer. So returned the negative value.\n",
    "    return -(5000*B-2000*A)\n",
    "\n",
    "def constraint(x):\n",
    "    return x[0]+x[1]-200\n",
    "\n",
    "#boundations\n",
    "\n",
    "b1 = [100, 200]     #bounds on A: 200 >= A >= 100\n",
    "b2 = [80, 170]      #bounds on B: 170 >= B >= 80\n",
    "\n",
    "bnds = (b1,b2)\n",
    "\n",
    "#defining Inequality type of constraint.\n",
    "con = {'type': 'ineq', 'fun': constraint}\n",
    "\n",
    "# passing any guess value for A and B into minimize fuinction.\n",
    "Xguess = [100,100]\n",
    "\n",
    "#Predicting Maximization values for the objective function by seeding guess value Xguess; boundations included..\n",
    "sol = minimize(objective, Xguess, method = 'SLSQP', options={'disp':True}, bounds = bnds, constraints = con)\n",
    "\n",
    "print('About solution from Optimize.minnimize: \\n' ,sol)\n",
    "\n",
    "\n",
    "#assigning values to desired results.\n",
    "profit = -sol.fun   #converting back to positive answer\n",
    "CarA = sol.x[0]     # number of car A models\n",
    "CarB = sol.x[1]     # number of car B models\n",
    "\n",
    "###################################################################\n",
    "\n",
    "print ('\\n\\n\\nPrinting the Results: \\n\\n\\n')\n",
    "print('maximum Profit Gained: $', profit)\n",
    "print('\\n Number of Model A Cars: ',CarA)\n",
    "print('\\n Number of Model B Cars: ',CarB)\n",
    "\n"
   ]
  },
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   "execution_count": null,
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