Supersport Footballs Inc manufactures three kinds of footbal

Supersport Footballs. Inc., manufactures three kinds of footballs: an All-Pro model, a College model, and a High School model. All three footballs require operations in the following departments: cutting and dyeing, sewing, and inspection and packaging. The production times and maximum production availabilities are shown here: Current orders indicate that at least 1000 All-Pro footballs must be manufactured. If Supersport realizes a profit contribution of $3 for each All-Pro model. $3 for each College model, and $4 for each High School model, how many footballs of each type should be produced? What occurs in the solution of this problem? Why? If Supersport can increase sewing time to 300 hours and inspection and packaging time to 150 hours by using overtime, what is your recommendation?

Solution

Answer:

Supersport Footballs, Inc. has the problem of determining the best number of Pro (P), College (C), and High-School (H) models of footballs to produce in order to maximize profits. Constraints include production capacity limitations in each of three departments (cutting and dyeing, sewing, and inspection and packaging) as well as a contractual obligation with the N.F.L. that requires production of at least 1000 Pro footballs. The linear programming model of Supersport’s problem is shown below:

The above linear program was solved using the Excel Solver. The resulting spreadsheet (already solved), along with the Sensitivity Report is shown below:

      For each of the following, answer the question as specifically and completely as is possible without re-solving the problem with the Solver. All problems are independent (i.e., any change made in one problem does not affect other problems).