! Ravinia Max Flow problem;
! One of the problems associated with the Ravinia festival
 in Highland Park in the summer is the management of the 
 associated traffic.  Electric signs are sometimes used to
 suggest routes to incoming motorists so as to evenly 
 utilize all available routes.  Below is a model for 
 finding the maximum possible flow per minute of cars
 into the main parking area for Ravinia.  Each decision 
 variable represents the traffic per minute on a one way street;
!Keywords: Max flow, Min cut, Traffic, Network;
MODEL:
  MAX = FE; ! Max flow/minute entering parking lot;
    [CLAVEY] F0 -F1 -F2                                = 0;
    [LKCOOK]        +F2     +F4 -F5             +F9    = 0; 
    [DUNDEE]            +F3             -F7 +F8        = 0;
    [BRODST]     F1     -F3 -F4     -F6                = 0;
    [MAINST]                    +F5 +F6 +F7         -FE= 0;
! Link capacities;
   [UB0] F0 <= 70;
   [UB1] F1 <= 45;
   [UB2] F2 <= 27;
   [UB3] F3 <= 22;
   [UB4] F4 <= 10;
   [UB5] F5 <= 40;
   [UB6] F6 <= 20;  
   [UB7] F7 <= 30; 
   [UB8] F8 <= 10;
   [UB9] F9 <= 20;
END

! The UB constraints with nonzero dual prices in the solution
  constitute a minimum cut or bottleneck, i.e., a set of arcs
  that partition the nodes into two sets, pre-bottleneck and 
  post bottleneck, for which the
  sum of the arc capacities is minimum;