{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nThe optimal value is 4.043281386825957e-10\nThe values of a and b are  57.94946776796661 28.97473388417445\n"
     ]
    }
   ],
   "source": [
    "import cvxpy as cp\n",
    "import numpy as np\n",
    "\n",
    "# declaring variables\n",
    "z = cp.Variable()\n",
    "a = cp.Variable()\n",
    "b = cp.Variable()\n",
    "\n",
    "# defining objective\n",
    "objective1 = cp.Minimize(z)\n",
    "\n",
    "# defining constraints\n",
    "constraints1 = [\n",
    "a-(2*b) <= z,\n",
    "(2*b)-a <= z,\n",
    "a+b >= 50,\n",
    "a >= 30,\n",
    "a <= 100,\n",
    "b <= 100,\n",
    "b >= 0\n",
    "]\n",
    "\n",
    "problem1 = cp.Problem(objective1, constraints1)\n",
    "problem1.solve()\n",
    "# printing outputs\n",
    "print(\"\\nThe optimal value is\", problem1.value)\n",
    "print(\"The values of a and b are \", a.value, b.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nThe optimal value is 3200.000001852015\nThe values of a and b are  -6.345394058853363e-08 500.00000006345397\n"
     ]
    }
   ],
   "source": [
    "import cvxpy as cp\n",
    "import numpy as np\n",
    "\n",
    "# declaring variables\n",
    "c_1 = cp.Variable()\n",
    "c_2 = cp.Variable()\n",
    "x = cp.Variable()\n",
    "\n",
    "# defining objective\n",
    "objective2 = cp.Minimize(c_1+c_2)\n",
    "\n",
    "# defining constraints\n",
    "constraints2 = [\n",
    "x >= 0,\n",
    "x <= 500,\n",
    "10*x <= c_1,    \n",
    "1200 <= c_2,\n",
    "1200 + 5*(400-x) <= c_2,\n",
    "]\n",
    "\n",
    "problem2 = cp.Problem(objective2, constraints2)\n",
    "problem2.solve()\n",
    "# printing outputs\n",
    "print(\"\\nThe optimal value is\", problem2.value)\n",
    "print(\"The values of a and b are \", x.value, 500-x.value)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.7.9 64-bit",
   "metadata": {
    "interpreter": {
     "hash": "e9752fd82d88768c444c24c0be54a259b62c17c2d80b41ed9b492f84bd073631"
    }
   }
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}