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.