The Spencer Shoe Company manufactures 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 the other two locations. Other data are as follows.
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Assume that Spencer Shoe Company will keep operating at Pontiac and build a plant at one of the three new alternatives. Which alternative will lead to the lowest total cost, including production, distribution, and fixed costs, and what is the minimum weekly cost?
Assume that Spencer Shoe Company could start from scratch and operate any combination of the four plants. Determine the plant locations that minimize total cost. Compared to the result in part (a), how much weekly cost could be saved with the optimal system design?

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Distributlon costs per palr from Demand (palrs/wk) To distributlon centers Pontlac CIncinnati Dayton Atlanta Milwaukee $0.42 $0.46 $0.44 $0.48 10,000 Dayton 15,000 0.36 0.37 0.30 0.45 Cincinnati 0.30 0.37 0.41 0.43 16,000 Buffalo 0.39 0.42 0.38 0.46 19,000 Atlanta 0.50 0.27 0.43 0.45 12,000 Capacity (pairs/wk) 32,000 40,000 40,000 40,000 Production cost/pair $2.70 $2.64 $2.69 $2.62 Fixed cost/wk S7000 $4000 $6000 $7000