Forbelt Corporation has one-year contract to provide motors for all refrigerators created by Ice Age Corporation. Ice Age manufactures the refrigerators at 4 locations around country:  Boston, Dallas, Los Angeles (LA), and St. Paul (SP). Plans call for the following number (in thousands) of refrigerators to be produced at each location:

Boston – 50K     Dallas – 70K     LA – 60K SP – 80K

Forbelt’s 3 plants are able of producing the motors. Plants and production capacities (in thousands) are:

Denver – 100k     Atlanta – 100     Chicago – 150

As of varying production and transportation costs, profit that Forbelt earns on each lot of 1000 units depends on which pant produced lot and which destination it was shipped to. Following table gives  accounting department estimates of profit per unit (shipments will be made in lots of 1000 units):

Shipped To

Produced At    Boston    Dallas    Los Angeles    St. Paul
Denver               7          11           8                  13
Atlanta              20         17          12                 10
Chicago             8           18          13                16

With profit maximization as the criterion, Forbelt’s management wishes to find out how many motors must be produced at each plant and how many motors must be shipped from each plant to each destination.

a) Develop a network representation of the model.

b) Find the optimal solution.