Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 900 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 Regular model Catcher's model Letting leads to the following formulation: Constraint 1 2 Optimal Objective Value = 3 Variable R с с Constraint 1 The sensitivity report is shown in the figure below. 2 Cutting and Sewing 3 1 3/2 Variable The sensitivity report is shown in the figure below. FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM R с Max s.t. R number of regular gloves C number of catcher's mitts = Regular Glove Catcher's Mitt Total Profit $ Finishing 1/2 ¹/3 5R + 8C 3/2C≤ 900 1/2+1/3Cs 300 1/8R+ ¹/4 Cs 100 R, C20 RHS Value 900.00000 300.00000 100.00000 3700.00000 Objective Coefficient 5.00000 8.00000 Optimal Solution Value 500.00000 150.00000 Slack/Surplus 175.00000 0.00000 0.00000 Packaging and Shipping 1/8 14 Allowable Increase Allowable Increase Infinite 100.00000 35.00000 7.00000 2.00000 Profit/Glove $5 88 Cutting and sewing Finishing Packaging and shipping Reduced Cost 0.00000 0.00000 Dual Value 0.00000 3.00000 28.00000 Allowable Decrease 175.00000 166.66667 25.00000 Allowable Decrease a. What is the optimal solution, and what is the value of the total profit contribution? 1.00000 4.66667
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 900 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 Regular model Catcher's model Letting leads to the following formulation: Constraint 1 2 Optimal Objective Value = 3 Variable R с с Constraint 1 The sensitivity report is shown in the figure below. 2 Cutting and Sewing 3 1 3/2 Variable The sensitivity report is shown in the figure below. FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM R с Max s.t. R number of regular gloves C number of catcher's mitts = Regular Glove Catcher's Mitt Total Profit $ Finishing 1/2 ¹/3 5R + 8C 3/2C≤ 900 1/2+1/3Cs 300 1/8R+ ¹/4 Cs 100 R, C20 RHS Value 900.00000 300.00000 100.00000 3700.00000 Objective Coefficient 5.00000 8.00000 Optimal Solution Value 500.00000 150.00000 Slack/Surplus 175.00000 0.00000 0.00000 Packaging and Shipping 1/8 14 Allowable Increase Allowable Increase Infinite 100.00000 35.00000 7.00000 2.00000 Profit/Glove $5 88 Cutting and sewing Finishing Packaging and shipping Reduced Cost 0.00000 0.00000 Dual Value 0.00000 3.00000 28.00000 Allowable Decrease 175.00000 166.66667 25.00000 Allowable Decrease a. What is the optimal solution, and what is the value of the total profit contribution? 1.00000 4.66667
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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