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

   file prodmix.mos
   ````````````````
   TYPE:         Product mix (single period production planning)
   DIFFICULTY:   1
   FEATURES:     simple LP problem
   DESCRIPTION:  A firm has 3 workshops, each working 40 hours per week, in
                 which it can produce two products. A unit of each product 
                 requires a given number of hours in the workshops and a 
                 given number of man hours. The hourly labor cost and the 
                 unit sales prices are known. The objective is to determine 
                 the most profitable operation.
   FURTHER INFO: "Applications of optimization with Xpress-MP", 
                 Section 2.3 "Simple resource constraints"

   (c) 2001 Dash Associates
       author: S. Heipcke
*******************************************************!)

model Workshop
 uses "mmxprs"                   ! Use Xpress-Optimizer

 declarations
  NProd = 2                      ! Number of products
  NShop = 3                      ! Number of workshops
  RP = 1..NProd
  RS = 1..NShop
  WMAX = 40	                 ! Maximum weekly working time 
  LABOR = 5                      ! Hourly labor cost 
  DUR: array(RP,RS) of integer   ! Duration of product p in shop s
  RES: array(RP) of integer      ! Man hours per unit
  PRICE: array(RP) of integer    ! Selling price per unit 
  make: array(RP) of mpvar          ! Amount of product p 
 end-declarations

 DUR  := [ 5, 9, 7,
          10, 2, 5]
 RES  := [10, 8]
 PRICE:= [108, 84]

                                 ! Objective: Maximize Benefit 
 MaxBen:= sum(p in RP) (PRICE(p)-LABOR*RES(p)) * make(p)
                              
 forall(s in RS)                 ! Limit on weekly working hours
  Capacity(s):= sum(p in RP) DUR(p,s)*make(p) <= WMAX

 maximize(MaxBen)

 writeln("Objective: ", getobjval)
 forall(p in RP) write("Product ", p, ":", getsol(make(p)), "  ")
 writeln
 
end-model