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Chapter 2: An Introduction to Linear Programming Question 2 (10 points): 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 a profit 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 Sewing 9A + 15C 25,200 6A + 6C 12,000 Inspection and Packaging A. C20 A portion of the graphical solution to the Reiser problem is shown in Figure. a. Shade the feasible region for this problem. b. Draw the profit line (objective 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. Which constraints are binding? Determine the coordinates of extreme point generates the highest profit? Calculate the highest profit? 3500 3000 Number of College Footb 2500 2000 1500 A portion of the graphical solution to the Reiser problem is shown in Figure. a. Shade the feasible region for this problem. b. Draw the profit line (objective 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. Which constraints are binding? Determine the coordinates of extreme point generates the highest profit? Calculate the highest profit? C A 1500 2000 1000 2500 Number of All-Pro Footballs Page 2 of 8 Number of College Footballs 3500 3000 2500 2000 1500 1000 500 0 500 3000

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