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Nonlinear objective with integer decision variables

The examples describe problems with a nonlinear objective function and some integer decision variables.
  1. A craftsman wants to optimise its revenue based on the size of the produced wooden boxes (boxes02.mos)
  2. Dealers sell apples at a market at the same price and the game is to find the quantity sold and the associated price (pricechange.mos).

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   Mosel NL examples
   file boxes02.mos
   A craftsman makes small wooden boxes for sale. 
   He has four different shapes or styles of box, and can make each of
   them in any size (keeping all the dimensions in proportion). 
   The profit he makes on a box depends on the size.   
   He has only a limited amount of the necessary wood available and a
   limited amount of time in the week to do the work.    
   How many boxes should he make, and what size should they be, 
   in order to maximize his profit?  
   (c) 2013 Fair Issac Corporation
       author: S. Heipcke, Nov. 2005, rev. Feb. 2013

model "Boxes"
 uses "mmxnlp"

  BOXES = {"Cube", "Oblong", "Flat", "Economy"}      ! Box types
  make: array(BOXES) of mpvar                        ! Number produced per box type
  size, battens, ply, profit, mtime: array(BOXES) of mpvar  ! Properties per box type
  LENGTH,WIDTH,HEIGHT,PROFIT,DUR: array(BOXES) of real      ! Length, width, height, profit, time
  TotalProfit: nlctr                                 ! Objective: total profit

 LENGTH :: (["Cube", "Oblong", "Flat", "Economy"])[1,1,4,1]
 WIDTH :: (["Cube", "Oblong", "Flat", "Economy"])[1,2,4,2]
 HEIGHT :: (["Cube", "Oblong", "Flat", "Economy"])[1,1,1,1]
 PROFIT :: (["Cube", "Oblong", "Flat", "Economy"])[20,27.3,90,10] ![20,24,90,10]
 DUR :: (["Cube", "Oblong", "Flat", "Economy"])[1,1,1,0.2]

 forall (b in BOXES) do
  battens(b) = 4*(LENGTH(b)+WIDTH(b)+HEIGHT(b))*size(b)
  ply(b) = 2*(LENGTH(b)*WIDTH(b)+WIDTH(b)*HEIGHT(b)+HEIGHT(b)*LENGTH(b))*size(b)^2
  profit(b) = PROFIT(b)*size(b)^1.5
  mtime(b) = 1 + DUR(b)*1.5^(ply(b)/10)

! Bounds on size and number of boxes
 forall(b in BOXES) do
  size(b) <= 2
  make(b) <= 6
  make(b) is_integer

! Limits on resource availability
 sum(b in BOXES) make(b)*battens(b) <= 200
 sum(b in BOXES) make(b)*ply(b) <= 210
 sum(b in BOXES) make(b)*mtime(b) <= 35

! Objective function: total profit
 TotalProfit := sum(B in BOXES) make(B)*profit(B)

 setparam("xnlp_verbose", true)

! Solve the problem

! Solution display
 forall (b in BOXES | make(b).sol>0) writeln(getsol(make(b)), " '", b,
  "' boxes of size ", getsol(size(b)),
  " each using ", getsol(battens(b)),
  " cm of battens, ", getsol(ply(b))," sq cm of plywood, ",
  strfmt(getsol(mtime(b)),0,2), " hours")
 writeln("\nTotal profit  ", getobjval)
 writeln("Total battens ",
  strfmt(getsol(sum(b in BOXES) make(b)*battens(b)),0,2)," cm")
 writeln("Total ply     ",
  strfmt(getsol(sum(b in BOXES) make(b)*ply(b)),0,2)," sq cm")
 writeln("Total mtime    ",
  strfmt(getsol(sum(b in BOXES) make(b)*mtime(b)),0,2)," hours")

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