Problem 8a

8. 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 num- ber (in thousands) of refrigerators to be produced at each location: Boston Dallas Los Angeles St. Paul 50 70 60 80 Forbelt's three plants are capable of producing the motors. The plants and production ca- pacities in thousands) are as follows: Denver Atlanta Chicago 100 100 150 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): Boston Dallas Produced At Denver Atlanta Chicago 7 20 8 Shipped To Los Angeles 8 12 13 11 17 18 St. Paul 13 10 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