text: # Copyright 2010-2021 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.
  
  # We are trying to group items in equal sized groups.
  # Each item has a color and a value. We want the sum of values of each group to
  # be as close to the average as possible.
  # Furthermore, if one color is an a group, at least k items with this color must
  # be in that group.
  
  
  from ortools.linear_solver import pywraplp
  
  import math
  
  # Data
  
  max_quantities = [["N_Total", 1944], ["P2O5", 1166.4], ["K2O", 1822.5],
                    ["CaO", 1458], ["MgO", 486], ["Fe", 9.7], ["B", 2.4]]
  
  chemical_set = [["A", 0, 0, 510, 540, 0, 0, 0], ["B", 110, 0, 0, 0, 160, 0, 0],
                  ["C", 61, 149, 384, 0, 30, 1,
                   0.2], ["D", 148, 70, 245, 0, 15, 1,
                          0.2], ["E", 160, 158, 161, 0, 10, 1, 0.2]]
  
  num_products = len(max_quantities)
  all_products = range(num_products)
  
  num_sets = len(chemical_set)
  all_sets = range(num_sets)
  
  # Model
  
  max_set = [
      min(max_quantities[q][1] / chemical_set[s][q + 1] for q in all_products
          if chemical_set[s][q + 1] != 0.0) for s in all_sets
  ]
  
  solver = pywraplp.Solver("chemical_set_lp",
                           pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
  
  set_vars = [solver.NumVar(0, max_set[s], "set_%i" % s) for s in all_sets]
  
  epsilon = solver.NumVar(0, 1000, "epsilon")
  
  for p in all_products:
      solver.Add(
          sum(chemical_set[s][p + 1] * set_vars[s]
              for s in all_sets) <= max_quantities[p][1])
      solver.Add(
          sum(chemical_set[s][p + 1] * set_vars[s]
              for s in all_sets) >= max_quantities[p][1] - epsilon)
  
  solver.Minimize(epsilon)
  
  print(("Number of variables = %d" % solver.NumVariables()))
  print(("Number of constraints = %d" % solver.NumConstraints()))
  
  result_status = solver.Solve()
  
  # The problem has an optimal solution.
  assert result_status == pywraplp.Solver.OPTIMAL
  
  assert solver.VerifySolution(1e-7, True)
  
  print(("Problem solved in %f milliseconds" % solver.wall_time()))
  
  # The objective value of the solution.
  print(("Optimal objective value = %f" % solver.Objective().Value()))
  
  for s in all_sets:
      print(
          "  %s = %f" % (chemical_set[s][0], set_vars[s].solution_value()),
          end=" ")
      print()
  for p in all_products:
      name = max_quantities[p][0]
      max_quantity = max_quantities[p][1]
      quantity = sum(
          set_vars[s].solution_value() * chemical_set[s][p + 1] for s in all_sets)
      print("%s: %f out of %f" % (name, quantity, max_quantity))
  