Problem 3-06 (Algorithmic) Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 1200 hours of production time available in its cutting and sewing department, 250 hours available in its finishing department, and 120 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Model Profit/Glove Production Time (hours) Cutting and Sewing Finishing 2 1/2 3/2 25 Regular model Packaging and Shipping 1/ 8 15 $8 Catcher's model $11 Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 8R + 11C s.t. 2R + 1200 Cutting and sewing + 3/2Cs 12 1/ R + 2/cs 1/8R+ 1/6Cs 12 CS 250 Finishing Packaging and shipping R, C20 The sensitivity report is shown in figure below. Optimal Objective Value = 6645.00000 Optimal Objective Value = 6645.00000 Value Variable ................ R Reduced Cost ................... 0.00000 40.00000 575.00000 C 0.00000 Constraint .... 1 Slack/Surplus ............ 257.50000 0.00000 0.00000 Dual Value ......... 0.00000 4.50000 46.00000 2 3 Variable .................. Objective Coefficient 8.00000 11.00000 ............ Allowable Increase 5.75000 1.80000 Allowable Decrease ............ 1.12500 4.60000 R Constraint RHS Value ......... 1200.00000 250.00000 120.00000 Allowable Increase ........ Infinite 1 Allowable Decrease ............ 257.50000 10.00000 57.50000 2 60.58820 5.00000 3 a. Determine the objective coefficients ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Objective Coefficient Range Variable lower limit upper limit Regular Glove Catcher's Mitt b. Interpret the ranges in part (a). As long as the profit per regular glove is the optimal solution of gloves will not change. Or as long as the profit per catcher's mitt is the optimal solution of gloves will not change. The assumption is that changed at the same time. C. Interpret the right-hand-side ranges. If there is no lower or upper limit, then enter the text "NA" as your answer. Round your answers to two decimal places. Enter "0" if your answer is zero. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging and Shipping As long as the number of hours available for cutting and sewing (Constraint 1) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for finishing (Constraint 2) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is As long as the number of hours available for packaging and shipping (Constraint 3) are the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is d. How much will the value of the optimal solution improve if 3 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Enter "0" if your answer is zero. Amount: $