Cases1(線性規(guī)劃案例答案1)

2.1a)Inthiscase,wehavetwodecisionvariables:thenumberofFamilyThrillseekersweshouldassembleandthenumberofClassyCruisersweshouldassemble.Wealsohavethefollowingthreeconstraints:Theplanthasamaximumof48,000laborhours.Theplanthasamaximumof20,000doorsavailable.ThenumberofCruisersweshouldassemblemustbelessthanorequalto3,500.ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$3,600$5,4004ResourcesResources5ResourceRequirementsUsedAvailable6laborHours610.548000<=48,00020,0007Doors4220000<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production3,8002.4001$2664000012<=Demand 3500 D4Resources5Used6SUMCDODUCT(B6：C6Eoduction)7=SUMFRODUCT(B7:C7,Poduotion) F10TotalProfit11=SUMPRODUCT(UnitProfitProduction)RangeFSmScensClassyCruisersC11DemandC13ProductionB11:C11ResourcesAvailableF6:F7ResourcesUsedD6:D7TotalProfitF11Rachel'splantshouldassemble3,800Thrillseekersand2,400Cruiserstoobtainamaximumprofitof$26,640,000.Inpart(a)above,weobservedthattheCruiserdemandconstraintwasnotbinding.Therefore,raisingthedemandfortheCruiserwillnotchangetheoptimalsolution.Themarketingcampaignshouldnotbeundertaken.Thenewvalueoftheright-handsideofthelaborconstraintbecomes48,000*1.25=60,000laborhours.AllformulasandSolversettingsusedinpart(a)remainthesame.ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$3,600$5,400—4—ResourcesResources5ResourceRequirements1IsedAvailable6laborHours610.556250<=60,00020,0007Doors4220000<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production3.2503.5001$3060000012<=Demand3500Rachel'splantshouldnowassemble3,250Thrillseekersand3,500Cruiserstoachieveamaximumprofitof$30,600,000.Usingovertimelaborincreasestheprofitby$30,600,000—$26,640,000=$3,960,000.Rachelshouldthereforebewillingtopayatmost$3,960,000extraforovertimelaborbeyondregulartimerates.Thevalueoftheright-handsideoftheCruiserdemandconstraintis3,500*1.20=4,200cars.Thevalueoftheright-handsideofthelaborhourconstraintis48,000*1.25=60,000hours.AllformulasandSolversettingsusedinpart(a)remainthesame.Ignoringthecostsoftheadvertisingcampaignandovertimelabor,ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$3,600$5,4004ResourcesResources5ResourceRequirementsUsedAvailable6laborHours610.560000<=60,00020,0007Doors4220000<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production3.0004.0001$3240000012<=Demand4200Rachel'splantshouldproduce3,000Thrillseekersand4,000Cruisersforamaximumprofitof$32,400,000.Thisprofitexcludesthecostsofadvertisingandusingovertimelabor.Theadvertisingcampaigncosts$500,000.Inthesolutiontopart(e)above,weusedthemaximumovertimelaboravailable,andthemaximumuseofovertimelaborcosts$1,600,000.Thus,oursolutioninpart(e)requiredanextra$500,000+$1,600,000=$2,100,000.Weperformthefollowingcost/benefitanalysis:Profitinpart(e):$32,400,000Advertisingandovertimecosts:$ 2,100,000$30,300,000Wecomparethe$30,300,000profitwiththe$26,640,000profitobtainedinpart(a)andconcludethatthedecisiontoruntheadvertisingcampaignanduseovertimelaborisaverywise,profitabledecision.

Becauseweconsiderthisquestionindependently,thevaluesoftheright-handsidesfortheCruiserdemandconstraintandthelaborhourconstraintarethesameasthoseinpart(a).WenowchangetheprofitfortheThrillseekerfrom$3,600to$2,800intheproblemformulation.AllformulasandSolversettingsusedinpart(a)remainthesame.ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$2,800 $5,4004ResourcesResources5—ResourceRequirementsUsedAvailable48,00020,0006laborHours6 10.54 248000<=7Doors14500<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production1.875 3,5001$24,150,00012—<=-4^Demand3500 Rachel'splantshouldassemble1,875Thrillseekersand3,500Cruiserstoobtainamaximumprofitof$24,150,000.Becauseweconsiderthisquestionindependently,theprofitfortheThrillseekerremainsthesameastheprofitspecifiedinpart(a).Thelaborhourconstraintchanges.EachThrillseekernowrequires7.5hoursforassembly.AllformulasandSolversettingsusedinpart(a)remainthesame.ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$3,600$5,400—4—ResourcesResources5ResourceRequirementsUsedAvailable6laborHours7.510.548000<=48,00020,0007Doors4213000<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production150035001$2430000012<=-43—Demand 3500 Rachel'splantshouldassemble1,500Thrillseekersand3,500Cruisersforamaximumprofitof$24,300,000.Becauseweconsiderthisquestionindependently,weusetheproblemformulationusedinpart(a).Inthisproblem,however,thenumberofCruisersassembledhastobestrictlyequaltothetotaldemand.Theformulasusedintheproblemformulationremainthesameasthoseusedinpart(a).ABCDEF1FamilyClassy2ThrillseekerCruiser3UnitProfit$3,600 $5,4004ResourcesResources5—ResourceRequirementsUsedAvailable48,00020,0006laborHours6 10.54 248000<=7Doors14500<=89FamilyClassy10ThrillseekerCruiserTotalProfit11Production1.875 3,5001$25,650,00012—-4^Demand3500 Thenewprofitis$25,650,000,whichis$26,640,000-$25,650,000=$990,000lessthantheprofitobtainedinpart(a).Thisdecreaseinprofitislessthan$2,000,000,soRachelshouldmeetthefulldemandfortheCruiser.Wenowcombinethenewconsiderationsdescribedinparts(f),(g),and(h).Inpart(f),wedecidedtouseboththeadvertisingcampaignandtheovertimelabor.TheadvertisingcampaignraisesthedemandfortheCruiserto4,200sedans,andtheovertimelaborincreasesthelaborhourcapacityoftheplantto60,000laborhours.Inpa