Module 2: LP Sensitivity Analysis (QUESTION 4)

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4. DETAILS ASWMSCI 15 3.E.005. Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C = number of catcher's mitts leads to the following formulation: Cutting and sewing Max 5R + 9C s.t. 3 R+ -C s 1,000 2 -R + Ic s 300 2 3 IR + 1 + -CS 100 8 4 RC 20 Finishing Packaging and shipping The computer solution is shown below. Optimal Objective Value = 3850.00000 Variable R Value 500.00000 150.00000 Reduced Cost 0.00000 0.00000 Constraint 1 2 3 Slack/Surplus 275.00000 0.00000 0.00000 Dual Value 0.00000 1.50000 34.00000 Variable Objective Coefficient 5.00000 9.00000 Allowable Increase 8.50000 1.00000 Allowable Decrease 0.50000 5.66667 R Constraint 1 RHS Value 1000.00000 300.00000 100.00000 Allowable Increase Infinite 100.00000 55.00000 Allowable Decrease 275.00000 166.66667 25.00000 2 3 (a) What is the optimal solution, and what is the value of the total profit contribution? regular glove catcher's mitt value (b) Which constraints are binding? (Select all that apply.) cutting and sewing finishing packaging and shipping (c) What are the dual values for the resources? Interpret each. constraint 1 Each additional hour of cutting and sewing will improve profits by $34.00. Each additional hour of cutting and sewing will improve profits by $275.00. Each additional hour of cutting and sewing will improve profits by $1.50. Additional hours of cutting and sewing will not improve profits. constraint 2 Each additional hour of finishing will improve profits by $34.00. Each additional hour of finishing will improve profits by $275.00. Each additional hour of finishing will improve profits by $1.50. Additional hours of finishing will not improve profits. constraint 3 Each additional hour of packing and shipping will improve profits by $34.00. Each additional hour of packing and shipping will improve profits by $275.00. Each additional hour of packing and shipping will improve profits by $1.50. Additional hours of packing and shipping will not improve profits. (d) If overtime can be scheduled in one of the departments, where would you recommend doing so? cutting and sewing finishing O packaging and shipping