1. The Freezing Cold Refrigerator Company has five production plants in Vancouver, Salem, Fresno, Bakersfield and Imperial. The harpsicords are all shipped to one of six distribution centers in Charlotte, Montreal, Philadelphia, Orlando, Hartford, and Augusta. The transportation costs between plants and distribution centers are as follows:

Charlotte Montreal Philadelphia Orlando Hartford Augusta

Vancouver 588 510 525 610 599 634

Salem 449 540 600 611 549 657

Fresno 482 590 625 595 608 721

Bakersfield 472 629 687 563 625 759

Imperial 454 612 721 586 656 801

The maximum capacity of the Vancouver plant is 120; the capacity of the Salem plant is 80; the capacity of the Fresno plant is 100; the capacity of the Bakersfield plant is 90; and the capacity of Imperial plant is 70. The minimum required shipments to Charlotte, Montreal, Philadelphia, Orlando, Hartford, and Augusta are 81, 60, 73, 92, 86, and 58, respectively.

a. The company's objective is to minimize the cost of transporting its product from its plants to its distribution center while satisfying the above constraints. Write out the objective function and the constraints.

b. Find the cost-minimizing solution using EXCEL's Solver. Hand in copies of the answer report and the sensitivity report.

c. How do you interpret the shadow prices for the capacity constraints? Would it be profitable to add another unit of capacity to the Vancouver plant if the cost of an additional unit of capacity is $50? Explain your answer with reference to the sensitivity report.

d. Explain the value of Salem's shadow price with reference to the changing pattern of shipments if Salem had one more unit of capacity available.

e. By how much could the cost of shipping from Salem to Augusta change by without changing your initial answer? Explain your answer with reference to the sensitivity report.