Reiser Sports Products wants to determine the number of All-Pro and College 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. The time required to manufacture the two types of footballs is shown in the following table: Labor Requirements (Hours) All-Pro College Cutting and Dyeing 3 4 Sewing 7 5 Inspection and Packaging 2 1 All-Pro footballs provide a profit of $5 per unit and College footballs provide a profit of $4 per unit. Formulate a linear optimization model that will maximize Reiser’s profits and satisfy the constraints.
Max 5A + 4C
12A + 6 C <= 20400
9A + 15C <= 25200
6X + 6Y <= 12000
x,y >= 0
a. shade the feasible region of this problem.
b. determined the coordinates of each extreme point and the corresponding profit. which extreme point generates the highest profit?
c. draw the profit line corresponding to 4000
d. which constraints are binding/ why?