(!*********************************************************************
   Mosel Example Problems
   ======================

   file prodx.mos
   ``````````````
   Simple production planning problem 
   
     Example discussed in section 2.5.1 of
     J. Kallrath: Business Optimization Using Mathematical Programming -
     An Introduction with Case Studies and Solutions in Various Algebraic 
     Modeling Languages. 2nd edition, Springer Nature, Cham, 2021 

   author: S. Heipcke, June 2018

   (c) Copyright 2020 Fair Isaac Corporation
  
    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.

*********************************************************************!) 

model 'prodx'
  uses "mmxprs"

  declarations
    PRODS=1..3                       ! Products
    RES=1..2                         ! Resources
    REQ: array(RES,PRODS) of real    ! Required machine hours
    PC: array(PRODS) of real         ! Profit contribution per product
  end-declarations

  REQ::[2.2, 1.8, 1.9,
        2.4, 2.0, 2.1]
  PC::[24.7, 22.4, 19.7]

  declarations
    a,b,c: mpvar     
  end-declarations

 ! Objective: maximise total profit
  Profit:= PC(1)*a + PC(2)*b + PC(3)*c

 ! Limits on resource availability
  M1:= REQ(1,1)*a + REQ(1,2)*b + REQ(1,3)*c<= 8
  M2:= REQ(2,1)*a + REQ(2,2)*b + REQ(2,3)*c<= 10

 ! Solve the problem
  maximise(Profit)
  writeln("Solution: Profit=", getobjval)
  writeln("  a=", a.sol, " b=", b.sol, " c=", c.sol)
end-model