Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher'smodel. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours availablein its finishing department, and 100 hours available in its packaging and shipping department. The production timerequirements and the profit contribution per glove are given in the following table:ModelRegular modelCatcher's modelLettingleads to the following formulation:VariableRC123Optimal Objective Value =Constraint123VariableConstraintCuttingand Sewing13/2RссMaxs.t.The sensitivity report is shown in the figure below.Regular GloveCatcher's MittTotal ProfitProduction Time (hours)R number of regular glovesC = number of catcher's mittsThe sensitivity report is shown in the figure below.FIGURE: THE SOLUTION FOR THE KELSON SPORTING EQUIPMENT PROBLEMFinishing1/21/3RHSValue900.00000300.00000100.00000SR + 8C+ ³/₂2 C≤ 9001/2R + ¹/3C≤ 3001/8R+ 1/4Cs 100R, C20R+3700.00000ValueOptimal Solution500.00000150.00000Slack/SurplusObjectiveCoefficient5.000008.00000175.000000.000000.00000Packagingand Shipping1/814AllowableIncreaseAllowableIncrease.Infinite100.0000035.000007.000002.00000Profit/Glove$5$8Cutting and sewingFinishingPackaging and shippingReduced Cost0.000000.00000Dual Value0.000003.0000028.00000AllowableDecrease175.00000166.6666725.00000AllowableDecreasea. What is the optimal solution, and what is the value of the total profit contribution?1.000004.66667 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 theunit.Cutting and sewing has a shadow price of $0cutting and sewing department the value ofobjective functionvariables, R and C,Cutting and sewing has a shadow price slack or surpluscutting and sewing department the valiconstraints 1, 2, and 3tion wouldFinishing has a shadow price of $department the value of the objective functi17528Finishing has a shadow price of $department the value of the objective function wouldFinishing has a shadow price of $department the value of the obje03Packaging and shipping has a sha28packaging and shipping departme175BindingNonbindingCutting and sewing has a shadow price of $cutting and sewing department the value of the objective function wouldFinishing has a shadow price of $department the value of the objective function wouldPackaging and shipping has a shadow price of $Cpackaging and shipping department the value.0will change by if you increase the constraint by oneConstraints with a shadow price of O means tha28175which means that if we add one hour to thewhich means that if we add one hour to thewouldans that if we add one hour to the finishingwhich means that if we add one hour to theCutting and sewingFinishingPackaging and shippingnot changewhich means that increase by $3increase by $28increase by $175which means that if we add one hour to the finishingnot changeincrease by $3Packaging and shipping has a shadow price of $packaging and shipping department the value of the increase by $28increase by $175which means that if we add one hour to thejective function wouldwhich means that if we add one hour to the finishingthe finishingmeans that if we add one hour to theldwhich means that if we add one hour to theIn wouldPackaging and shipping has a shadow price of $which means that if we add one hour to thepackaging and shipping department the value of the objective function would (Constraints with a shadow price of O means thatnot changeincrease by $3increase by $28If overtime can be scheduled in one of the departments, where would you recincrease by $175Constraints with a shadow price of O means that IIf overtime can be scheduled in one of the departit is a binding constraintit is a nonbinding constraintnd doing so?a mistake has been madeo hours of that constraint are usedd. If overtime can be scheduled in one of the departments, where would you recommend doing so?

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

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...