! University of Illinois at Urbana-Champaign
! MATH-484 - Fall 2013
! Instructor Bernard Lidicky
!

! First try version

! Paste this file to http://apmonitor.com/online/view_pass.php
!
! pipes problem
! 400pcs of 50cm pipes
! 100pcs of 65cm pipes
!
! How to cut the pipes if two 15 cm and one 20cm pipe is needed for
! manufacturing a final product? Maximize the number of final products.
! 
! A ... # 15cm after cutting
! B ... # 30cm after cutting
!
! x[1] 15+15+20    2A+B
! x[2] 20+20       2B
! x[3] 15+15+15    3A
!
! y[1] 20+20+20     3B
! y[2] 15+15+15+15   4A
! y[3] 20+15+15+15   B+3A
! y[4] 20+20+15      2B+A
!


Model pipes
  Variables
    x[1] = 0
    x[2] = 0
    x[3] = 0
    y[1] = 0
    y[2] = 0
    y[3] = 0
    y[4] = 0
    a = 0
    b = 0
    c = 0
  End Variables

  Equations
    x[1]+x[2]+x[3] <= 400
    y[1]+y[2]+y[3]+y[4] <= 100

    a = 2*x[1]+3*x[2]+4*y[2]+3*y[3]+y[4]
    b = 2*x[1]+2*x[2]+3*y[1]+y[3]+2*y[4]    

    c <= 0.5*a
    c <= b

    a >= 0
    b >= 0
    x[1] >= 0
    x[2] >= 0
    x[3] >= 0
    y[1] >= 0
    y[2] >= 0
    y[3] >= 0
    y[4] >= 0

    maximize c
  End Equations
End Model