Supersport Footballs, Inc. has to determine the best number of All-Pro (A)

January 30, 2017

Question
Supersport Footballs, Inc. has to determine the best number of All-Pro (A), College (C),and High School (H) models of footballs to produce in order to maximize profits.Constraints include production capacity limitations (time available in minutes) in each ofthree departments (cutting and dyeing, sewing, and inspection and packaging) as well asa constraint that requires the production of at least 1000 All-Pro footballs. The linearprogramming model of Supersportâ€™s problem isMax z =3A + 5C +4Hs.t.12A +10C + 8 H ? 18,000 Cutting and dyeing15A + 15C+ 12H ? 18,000 Sewing 3A + 4C+ 2H ? 9,000 Inspection and packaging 1A ? 1,000 All-Pro modelA, C, H ? 0Refer to the enclosed Excel computer solution and answer the following:

a. (10 points) Overtime rates in the sewing department are \$12 per hour. Would yourecommend that the company consider using overtime in that department? Explain.

b. (10 points) What is the shadow price for the fourth constraint? Interpret its value formanagement.

c. (10 points) Suppose that the profit contribution of the College ball is increased by \$1.How do you expect the solution to change?

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