{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Copyright 2010-2018 Google LLC\n",
    "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "# you may not use this file except in compliance with the License.\n",
    "# You may obtain a copy of the License at\n",
    "#\n",
    "#     http://www.apache.org/licenses/LICENSE-2.0\n",
    "#\n",
    "# Unless required by applicable law or agreed to in writing, software\n",
    "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "# See the License for the specific language governing permissions and\n",
    "# limitations under the License.\n",
    "\"\"\"Small example to illustrate solving a MIP problem.\"\"\"\n",
    "# [START program]\n",
    "from __future__ import print_function\n",
    "# [START import]\n",
    "from ortools.linear_solver import pywraplp\n",
    "# [END import]\n",
    "\n",
    "\n",
    "def IntegerProgrammingExample():\n",
    "    \"\"\"Integer programming sample.\"\"\"\n",
    "    # [START solver]\n",
    "    # Create the mip solver with the CBC backend.\n",
    "    solver = pywraplp.Solver('IntegerProgrammingExample',\n",
    "                             pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)\n",
    "    # [END solver]\n",
    "\n",
    "    # [START variables]\n",
    "    # x, y, and z are non-negative integer variables.\n",
    "    x = solver.IntVar(0.0, solver.infinity(), 'x')\n",
    "    y = solver.IntVar(0.0, solver.infinity(), 'y')\n",
    "    z = solver.IntVar(0.0, solver.infinity(), 'z')\n",
    "    # [END variables]\n",
    "\n",
    "    # [START constraints]\n",
    "    # 2*x + 7*y + 3*z <= 50\n",
    "    constraint0 = solver.Constraint(-solver.infinity(), 50)\n",
    "    constraint0.SetCoefficient(x, 2)\n",
    "    constraint0.SetCoefficient(y, 7)\n",
    "    constraint0.SetCoefficient(z, 3)\n",
    "\n",
    "    # 3*x - 5*y + 7*z <= 45\n",
    "    constraint1 = solver.Constraint(-solver.infinity(), 45)\n",
    "    constraint1.SetCoefficient(x, 3)\n",
    "    constraint1.SetCoefficient(y, -5)\n",
    "    constraint1.SetCoefficient(z, 7)\n",
    "\n",
    "    # 5*x + 2*y - 6*z <= 37\n",
    "    constraint2 = solver.Constraint(-solver.infinity(), 37)\n",
    "    constraint2.SetCoefficient(x, 5)\n",
    "    constraint2.SetCoefficient(y, 2)\n",
    "    constraint2.SetCoefficient(z, -6)\n",
    "    # [END constraints]\n",
    "\n",
    "    # [START objective]\n",
    "    # Maximize 2*x + 2*y + 3*z\n",
    "    objective = solver.Objective()\n",
    "    objective.SetCoefficient(x, 2)\n",
    "    objective.SetCoefficient(y, 2)\n",
    "    objective.SetCoefficient(z, 3)\n",
    "    objective.SetMaximization()\n",
    "    # [END objective]\n",
    "\n",
    "    # Solve the problem and print the solution.\n",
    "    # [START print_solution]\n",
    "    solver.Solve()\n",
    "    # Print the objective value of the solution.\n",
    "    print('Maximum objective function value = %d' % solver.Objective().Value())\n",
    "    print()\n",
    "    # Print the value of each variable in the solution.\n",
    "    for variable in [x, y, z]:\n",
    "        print('%s = %d' % (variable.name(), variable.solution_value()))\n",
    "    # [END print_solution]\n",
    "\n",
    "\n",
    "IntegerProgrammingExample()\n",
    "# [END program]\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 4
}