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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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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: Model Regular model Catcher's model Letting leads to the following formulation: Variable R C 1 2 3 Optimal Objective Value = Constraint 1 2 3 Variable Constraint Cutting and Sewing 1 3/2 R с с Max s.t. The sensitivity report is shown in the figure below. Regular Glove Catcher's Mitt Total Profit Production Time (hours) R number of regular gloves C = number of catcher's mitts The sensitivity report is shown in the figure below. FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM Finishing 1/2 1/3 RHS Value 900.00000 300.00000 100.00000 SR + 8C + ³/₂2 C≤ 900 1/2R + ¹/3C≤ 300 1/8R+ 1/4Cs 100 R, C20 R+ 3700.00000 Value Optimal Solution 500.00000 150.00000 Slack/Surplus Objective Coefficient 5.00000 8.00000 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 $8 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
Transcribed Image Text: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: Model Regular model Catcher's model Letting leads to the following formulation: Variable R C 1 2 3 Optimal Objective Value = Constraint 1 2 3 Variable Constraint Cutting and Sewing 1 3/2 R с с Max s.t. The sensitivity report is shown in the figure below. Regular Glove Catcher's Mitt Total Profit Production Time (hours) R number of regular gloves C = number of catcher's mitts The sensitivity report is shown in the figure below. FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEM Finishing 1/2 1/3 RHS Value 900.00000 300.00000 100.00000 SR + 8C + ³/₂2 C≤ 900 1/2R + ¹/3C≤ 300 1/8R+ 1/4Cs 100 R, C20 R+ 3700.00000 Value Optimal Solution 500.00000 150.00000 Slack/Surplus Objective Coefficient 5.00000 8.00000 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 $8 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
b. Which constraints are binding? Cutting and Sewing: Finishing: Packaging and shipping: c. What are the shadow prices for the resources? Cutting and Sewing: Finishing: Packaging and shipping: $ The shadow price is the value that the unit. Cutting and sewing has a shadow price of $0 cutting and sewing department the value of objective function variables, R and C, Cutting and sewing has a shadow price slack or surplus cutting and sewing department the valiconstraints 1, 2, and 3tion would Finishing has a shadow price of $ department the value of the objective functi175 28 Finishing has a shadow price of $ department the value of the objective function would Finishing has a shadow price of $ department the value of the obje 0 3 Packaging and shipping has a sha28 packaging and shipping departme175 Binding Nonbinding Cutting and sewing has a shadow price of $ cutting and sewing department the value of the objective function would Finishing has a shadow price of $ department the value of the objective function would Packaging and shipping has a shadow price of $C packaging and shipping department the value. 0 will change by if you increase the constraint by one Constraints with a shadow price of O means tha28 175 which means that if we add one hour to the which means that if we add one hour to the would ans that if we add one hour to the finishing which means that if we add one hour to the Cutting and sewing Finishing Packaging and shipping not change which means that increase by $3 increase by $28 increase by $175 which means that if we add one hour to the finishing not change increase by $3 Packaging and shipping has a shadow price of $ packaging and shipping department the value of the increase by $28 increase by $175 which means that if we add one hour to the jective function would which means that if we add one hour to the finishing the finishing means that if we add one hour to the ld which means that if we add one hour to the In would Packaging and shipping has a shadow price of $ which means that if we add one hour to the packaging and shipping department the value of the objective function would ( Constraints with a shadow price of O means that not change increase by $3 increase by $28 If overtime can be scheduled in one of the departments, where would you recincrease by $175 Constraints with a shadow price of O means that I If overtime can be scheduled in one of the departit is a binding constraint it is a nonbinding constraint nd doing so? a mistake has been made o hours of that constraint are used d. If overtime can be scheduled in one of the departments, where would you recommend doing so?
Transcribed Image Text:b. Which constraints are binding? Cutting and Sewing: Finishing: Packaging and shipping: c. What are the shadow prices for the resources? Cutting and Sewing: Finishing: Packaging and shipping: $ The shadow price is the value that the unit. Cutting and sewing has a shadow price of $0 cutting and sewing department the value of objective function variables, R and C, Cutting and sewing has a shadow price slack or surplus cutting and sewing department the valiconstraints 1, 2, and 3tion would Finishing has a shadow price of $ department the value of the objective functi175 28 Finishing has a shadow price of $ department the value of the objective function would Finishing has a shadow price of $ department the value of the obje 0 3 Packaging and shipping has a sha28 packaging and shipping departme175 Binding Nonbinding Cutting and sewing has a shadow price of $ cutting and sewing department the value of the objective function would Finishing has a shadow price of $ department the value of the objective function would Packaging and shipping has a shadow price of $C packaging and shipping department the value. 0 will change by if you increase the constraint by one Constraints with a shadow price of O means tha28 175 which means that if we add one hour to the which means that if we add one hour to the would ans that if we add one hour to the finishing which means that if we add one hour to the Cutting and sewing Finishing Packaging and shipping not change which means that increase by $3 increase by $28 increase by $175 which means that if we add one hour to the finishing not change increase by $3 Packaging and shipping has a shadow price of $ packaging and shipping department the value of the increase by $28 increase by $175 which means that if we add one hour to the jective function would which means that if we add one hour to the finishing the finishing means that if we add one hour to the ld which means that if we add one hour to the In would Packaging and shipping has a shadow price of $ which means that if we add one hour to the packaging and shipping department the value of the objective function would ( Constraints with a shadow price of O means that not change increase by $3 increase by $28 If overtime can be scheduled in one of the departments, where would you recincrease by $175 Constraints with a shadow price of O means that I If overtime can be scheduled in one of the departit is a binding constraint it is a nonbinding constraint nd doing so? a mistake has been made o hours of that constraint are used d. If overtime can be scheduled in one of the departments, where would you recommend doing so?
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ISBN:
9781337406659
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WINSTON, Wayne L.
Publisher:
Cengage,
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