Refer to the Kelson Sporting Equipment problem (Chapter 2, Problem 24). Letting
R = number of regular gloves
C = number of catcher's mitts
Leads to the following formulation:
Max 5R + 8C
s.t.
R + 3/2C ‰¤ 900 Cutting and sewing
1/2R + 1/3C ‰¤ 300 Finishing
1/8R + 1/4C ‰¤ 100 Packaging and shipping
R, C ‰¥ 0
The computer solution is shown in Figure 3.13.
a. What is the optimal solution, and what is the value of the total profit contribution?
b. Which constraints are binding?
c. What are the dual values for the resources? Interpret each.
d. If overtime can be scheduled in one of the departments, where would you recommend doing so?
Figure 3.13

Optimal Objective Value - 3700.00000 Variable Value Reduced Cost 500.00000 150.00000 0.00000 0.00000 Constraint Slack/Surplus Dual Value 175.00000 0.00000 0.00000 0.00000 3.00000 28.00000 Objective Coefficient Allowable Increase Allowable Variable Decrease 5.00000 8.00000 7.00000 2.00000 1.00000 4.66667 RHS Value Allowable Increase Allowable Decrease Constraint 900.00000 300.00000 100.00000 1 Infinite 100.00000 35.00000 175.00000 166.66667 25.00000