# Quantitative Methods

**Topics:**Optimization, Linear programming, Operations research

**Pages:**2 (291 words)

**Published:**November 21, 2012

Please show all your work with the problems in steps but NOT just answers.

22. Reiser Sports Products wants to determine the number of All-Pro (A) and College (C) footballs to produce in order to maximize profit over the next four-week planning horizon. Constraints affecting the production quantities are the production capacities in three departments: cutting and dyeing; sewing; and inspection and packaging. For the four-week planning period, 340 hours of cutting and dyeing time, 420 hours of sewing time, and 200 hours of inspection and packaging time are available. All-Pro footballs provide of $5 per unit and College footballs provide a profit of $4 per unit. The linear programming model with production times expressed in minutes is as follows:

Max 5A + 4C

s.t.

12A + 6C 20,400 Cutting and dyeing

9A + 15C 25,200 Sewing

6A + 6C 12,000 Inspection and packaging

A, C 0

A portion of the graphical solution to the Reiser problem is shown in Figure 2.23 a. Shade the feasible region for this problem.

b. Determine the coordinates of each extreme point and the corresponding profit. Which extreme point generates the highest profit?

c. Draw the profit line corresponding to a profit of $4000. Move the profit line as far from the origin as you can in order to determine which extreme point will provide the optimal solution. Compare your answer with the approach you used in part (b).

d. Which constraints are binding? Explain.

e. Suppose that the values of the objective function coefficients are $4 for each All-Pro model produced and $5 for each College model. Use the graphical solution procedure to determine the new optimal solution and the corresponding value of profit.

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