Question: Supersport Footballs, Inc., has to determine the best number of All­Pro (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 of three departments (cutting and dyeing, sewing, and inspection and packaging) as well as constraint that requires the production of at least 1000 All­Pro footballs. The linear programming model of Supersport’s problem is shown here:

Max z = 3A+5C+4H

Subject to:

12A + 1 0C + 8H≤18,000 Cutting and dying

15A + 15C + 12H ≤ 18,000 Sewing

3A + 4C + 24H ≤ 9,000 Inspection and modeling

1A ≥ 1,000 Al­Pro model

A,C,H≥0

Solve the problem using Excel Solver.

a) How many footballs of each type should Supersport produce to maximize the total profit contribution?

b) Which constraints are binding?

c) Interpret slack and/or surplus in each constraint.

d) Overtime rates in the sewing department are $12 per hour. Would you recommend that the company consider using overtime in that department? Explain.

e) What is the shadow price for the fourth constraint? Interpret its value for management.

f) Suppose that the profit contribution of the College ball is increased by $1. How do you expect the solution to change? What is the new value of the objective function (profit)?