Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the Ice Age Corporation. Ice Age manufactures the refrigerators at four locations around the country: Boston. Dallas. Los Angeles. and St. Paul. Plans call for the following number (in thousands) of refrigerators to be produced at each location:
|
Boston
|
50
|
|
Dallas
|
70
|
|
Los Angeles
|
60
|
|
St. Paul
|
80
|
Forbeles three plants are capable of producing the motors. The plants and production capacities (in thousands) are as follows:
|
Denver
|
100
|
|
Atlanta
|
100
|
|
Chicago
|
150
|
Because of varying production and transportation costs, the profit that Forbelt earns on each lot of 1000 units depends on which plant produced the lot and which destination it was shipped to. The following table gives the accounting department estimates of the 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
|
1 3
|
|
Atlanta
|
20
|
17
|
12
|
10
|
|
Chicago
|
8
|
18
|
13
|
16
|
With profit maximization as a criterion, Forbelt's management wants to determine how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination.
a. Develop a network representation of this problem.
b. Find the optimal solution.