Reference no: EM131153114
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) Model Cutting and Sewing Finishing Packaging and Shipping Profit/Glove Regular model 1 Catcher`s model Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Max 8R + 11C s.t. R + C ≤ 600 Cutting and sewing R + C ≤ 300 Finishing R + C ≤ 100 Packaging and shipping R, C ≥ 0 The sensitivity report is shown in figure below. Optimal Objective Value = 3800.00000 Variable Value Reduced Cost R 295.65220 0.00000 C 130.43480 0.00000 Constraint Slack/Surplus Dual Value 1 0.00000 3.00000 2 65.21740 0.00000 3 0.00000 20.00000 Variable Objective Coefficient Allowable Increase Allowable Decrease R 8.00000 5.75000 3.28570 C 11.00000 7.66670 4.60000 Constraint RHS Value Allowable Increase Allowable Decrease 1 600.00000 374.99990 200.00000 2 300.00000 Infinite 65.21740 3 100.00000 50.00000 48.57140
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.
Interpret the ranges in part (a.). As long as the profit per regular glove is between $8.00 and $13.75 the optimal solution of 295.6522 regular and 130.4348 catcher gloves will not change. Or as long as the profit per catcher glove is between $4.60 and $18.67 the optimal solution of 295.6522 regular and 130.4348 catcher gloves will not change. The assumption is that only one variable is changed at a/the same time.
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. Constraint Right-Hand-Side Range lower limit upper limit Cutting and Sewing Finishing Packaging As long as the number of hours available for cutting and sewing (Constraint 1) are between 400.00 and 975.00 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 65.22 or above 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 (Constraint 3) are between 100.00 and 150.00 the change in the optimal value of the solution per unit increase in the right-hand side of the constraint is .
How much will the value of the optimal solution improve if 5 extra hours of packaging and shipping time are made available? If required, round your answer to three decimal places. Amount: $
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