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   "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",
    "\"\"\"Linear optimization example.\"\"\"\n",
    "# [START program]\n",
    "from __future__ import print_function\n",
    "# [START import]\n",
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "# [END import]\n",
    "\n",
    "\n",
    "def LinearProgrammingExample():\n",
    "    \"\"\"Linear programming sample.\"\"\"\n",
    "    # Instantiate a Glop solver, naming it LinearExample.\n",
    "    # [START solver]\n",
    "    solver = pywraplp.Solver('LinearProgrammingExample',\n",
    "                             pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)\n",
    "    # [END solver]\n",
    "\n",
    "    # Create the two variables and let them take on any non-negative value.\n",
    "    # [START variables]\n",
    "    x = solver.NumVar(0, solver.infinity(), 'x')\n",
    "    y = solver.NumVar(0, solver.infinity(), 'y')\n",
    "    # [END variables]\n",
    "\n",
    "    # [START constraints]\n",
    "    # Constraint 0: x + 2y <= 14.\n",
    "    constraint0 = solver.Constraint(-solver.infinity(), 14)\n",
    "    constraint0.SetCoefficient(x, 1)\n",
    "    constraint0.SetCoefficient(y, 2)\n",
    "\n",
    "    # Constraint 1: 3x - y >= 0.\n",
    "    constraint1 = solver.Constraint(0, solver.infinity())\n",
    "    constraint1.SetCoefficient(x, 3)\n",
    "    constraint1.SetCoefficient(y, -1)\n",
    "\n",
    "    # Constraint 2: x - y <= 2.\n",
    "    constraint2 = solver.Constraint(-solver.infinity(), 2)\n",
    "    constraint2.SetCoefficient(x, 1)\n",
    "    constraint2.SetCoefficient(y, -1)\n",
    "    # [END constraints]\n",
    "\n",
    "    # [START objective]\n",
    "    # Objective function: 3x + 4y.\n",
    "    objective = solver.Objective()\n",
    "    objective.SetCoefficient(x, 3)\n",
    "    objective.SetCoefficient(y, 4)\n",
    "    objective.SetMaximization()\n",
    "    # [END objective]\n",
    "\n",
    "    # Solve the system.\n",
    "    # [START solve]\n",
    "    solver.Solve()\n",
    "    # [END solve]\n",
    "    # [START print_solution]\n",
    "    opt_solution = 3 * x.solution_value() + 4 * y.solution_value()\n",
    "    print('Number of variables =', solver.NumVariables())\n",
    "    print('Number of constraints =', solver.NumConstraints())\n",
    "    # The value of each variable in the solution.\n",
    "    print('Solution:')\n",
    "    print('x = ', x.solution_value())\n",
    "    print('y = ', y.solution_value())\n",
    "    # The objective value of the solution.\n",
    "    print('Optimal objective value =', opt_solution)\n",
    "    # [END print_solution]\n",
    "\n",
    "\n",
    "LinearProgrammingExample()\n",
    "# [END program]\n",
    "\n"
   ]
  }
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