# Copyright 2010-2018 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""Linear optimization example."""
# [START program]
from __future__ import print_function
# [START import]
from ortools.linear_solver import pywraplp

# [END import]


def LinearProgrammingExample():
    """Linear programming sample."""
    # Instantiate a Glop solver, naming it LinearExample.
    # [START solver]
    solver = pywraplp.Solver.CreateSolver('linear_programming_examples', 'glop')
    # [END solver]

    # Create the two variables and let them take on any non-negative value.
    # [START variables]
    x = solver.NumVar(0, solver.infinity(), 'x')
    y = solver.NumVar(0, solver.infinity(), 'y')
    # [END variables]

    # [START constraints]
    # Constraint 0: x + 2y <= 14.
    constraint0 = solver.Constraint(-solver.infinity(), 14)
    constraint0.SetCoefficient(x, 1)
    constraint0.SetCoefficient(y, 2)

    # Constraint 1: 3x - y >= 0.
    constraint1 = solver.Constraint(0, solver.infinity())
    constraint1.SetCoefficient(x, 3)
    constraint1.SetCoefficient(y, -1)

    # Constraint 2: x - y <= 2.
    constraint2 = solver.Constraint(-solver.infinity(), 2)
    constraint2.SetCoefficient(x, 1)
    constraint2.SetCoefficient(y, -1)
    # [END constraints]

    # [START objective]
    # Objective function: 3x + 4y.
    objective = solver.Objective()
    objective.SetCoefficient(x, 3)
    objective.SetCoefficient(y, 4)
    objective.SetMaximization()
    # [END objective]

    # Solve the system.
    # [START solve]
    solver.Solve()
    # [END solve]
    # [START print_solution]
    opt_solution = 3 * x.solution_value() + 4 * y.solution_value()
    print('Number of variables =', solver.NumVariables())
    print('Number of constraints =', solver.NumConstraints())
    # The value of each variable in the solution.
    print('Solution:')
    print('x = ', x.solution_value())
    print('y = ', y.solution_value())
    # The objective value of the solution.
    print('Optimal objective value =', opt_solution)
    # [END print_solution]


LinearProgrammingExample()
# [END program]