1. The Better Widgets 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:

The maximum capacity of the Vancouver plant is 122; the capacity of the Salem plant is 81; the

capacity of the Fresno plant is 103; the capacity of the Bakersfield plant is 89; and the capacity

of Imperial plant is 68. The minimum required shipments to Charlotte, Montreal, Philadelphia,

Orlando, Hartford, and Augusta are 82, 61, 77, 90, 84, 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 $51? 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.