Processing Time (hr) Product Department A Department B Material (yd) Shirts Shorts 2 3 1 Pants 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 Xy = 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 2 = 15 X + 15 X2 + 30 X, Constraints: Department A: 2X2 + 2x + 3X, s 120 Department B: 1 X + 3x + 4 S 150 Material: 2 X+ 1 X+ 4X, S 100 Nonnegativity: X. X. 20 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.)