XYZ Corporation has a one-year contract to supply motors for all refrigerators produced by the IA Corporation. IA 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

100

Dallas

80

Los Angeles

100

St. Paul

70

XYZ's three plants are capable of producing the motors. The plants and production capacities (in thousands) are as follows:

Denver

80

Atlanta

200

Chicago

150

Because of varying production and transportation costs, the profit that XYZ 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

8

18

13

10

Atlanta

20

17

8

13

Chicago

7

11

15

16

With profit maximization as a criterion, XYZ'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.

1. (20 p.) Find the optimal solution and the maximum profit.

2. (20 p.) In which plant there will be idle capacity and how many units (in thousands)?

3. (10 p.) Does optimal solutions exist? Justify your answer.

4. (30 p.) If they exist, use the stepping stone algorithm and find the second optimal solution. Present your analysis in a graphically neat manner. Use any drawing technique you like - just make sure it looks fairly professional.

5. (20 p.) Produce the third optimal solution by taking a combination of 20% of the first optimal solution and 80% of the second one.

Attach all relevant exhibits from Excel's Solver calculations. Use PrintScreen, edit/copy/paste, etc. - whatever you like.