Department A has 120 hours of capacity, department B has 150 hours of capacity, and 100 yards of material are available. Each shirt contributes $15 to profits and overhead; each pair of shorts, $15; and each pair of pants, $30. a. Let X, = number of shirts produced, X = number of shorts produced, X = number of pants produced. Specify the objective function and constraints for the problem. Objective function: Maximize Z = 15 X, + 15 X + 30 X, Constraints: Department A: 2 x, + 2 X + 3 X, s 120 1 X, + 3 X + 4 X, s 150 2 X, + 1 X2 + 4 X3s 100 Department B: Material: Nonnegativity: X4, Xg z 0 b. A linear programming software shows that all three constraints are binding. The optimal solution is (enter your responses rounded to two decimal places): X, = 12.22. X = 31.11. X, = 11.11. c. How much should Astaire be willing to pay for an extra hour of department A capacity? Astaire should be willing to add an extra hour of department A capacity if its cost were less than (Enter your response rounded to the nearest cent.) Processing Time (hr) Product Department A Department B Material (yd) Shirts Shorts Pants 3 4 2 14 N23