The Spencer Shoe Company manufacturers a line of inexpensive shoes in one plant in Pontiac and distributes to five main distribution centers (Milwaukee, Dayton, Cincinnati, Buffalo, and Atlanta) from which the shoes are shipped to retail shoe stores. Distribution costs include freight, handling, and warehousing costs. To meet increased demand, the company has decided to build at least one new plant with a capacity of 40,000 pairs per week. Surveys have narrowed the choice to three locations: Cincinnati, Dayton, and Atlanta. As expected, production costs would be low in the Atlanta plant, but distribution costs are relatively high compared to those of the other two locations. Other data are as follows:

a. Assume that the Pontiac plant has no resale value and must remain open. What are the plant locations that will minimize total costs, including production, distribution, and fixed costs? What is the optimal total cost?
b. Assume that the Pontiac plant could be closed at zero net cost. What are the optimal locations? What is the optimal total cost?