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 600 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (hours) Cutting and Sewing Finishing Packaging and Shipping Model Profit/Glove Regular model 1 1/2 23 1/4 $8 Catcher`s model $11 3 Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 8R + 11C s.t. R + Cutting and sewing 73c5 60 1/2R+ 23cs 30 1/R + cs 100 Finishing Packaging and shipping R, C20 The sensitivity renart is shown in figure helow The sensitivity report is shown in figure below. Optimal Objective Value = 3800.00000 Variable Value Reduced Cost R 0.00000 295.65220 130.43480 0.00000 Constraint Dual Value Slack/Surplus 0.00000 1 3.00000 65.21740 0.00000 2 3 0.00000 20.00000 Variable Objective Coefficient 8.00000 Allowable Decrease Allowable Increase 5.75000 7.66670 R 3.28570 C 11.00000 4.60000 RHS Allowable Constraint Allowable Increase Decrease 1 200.00000 Value 600.00000 300.00000 100.00000 374.99990 Infinite 65.21740 2 3 50.00000 48.57140 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 4.71 13.7 Catcher's Mitt 6.40000 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 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 10 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: $