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

Forbelt has three plants that are capable of producing the motors. The plants and productions capacities (in thousands) are:

Denver: 100
Atlanta: 100
Chicago: 150

Because of varying production and transportation cost, 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 fives the accounting department estimates of the profit per lot (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 10

With profit maximization as a criterion, Forbelt 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) Write a linear programming formulation of this problem.
(b) Find the optimal solution by using Excel. Include the computer output.