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

! Better 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
  Parameters
    p[1] = 400
    p[2] = 100
  End Parameters

  Variables
  ! if name of a variable starts with int, it is treated as an integer variable in APMonitor
    intx[1:3] = 0, >= 0
    inty[1:4] = 0, >= 0
    a = 0, >= 0
    b = 0, >= 0
    c = 0, >= 0
  End Variables

  Equations
    intx[1]+intx[2]+intx[3] <= p[1]
    inty[1]+inty[2]+inty[3]+inty[4] <= p[2]

    a = 2*intx[1]+3*intx[2]+4*inty[2]+3*inty[3]+inty[4]
    b = 2*intx[1]+2*intx[2]+3*inty[1]+inty[3]+2*inty[4]    

    c <= 0.5*a
    c <= b

    maximize c
  End Equations
End Model