Introduction to Mathematical Programming.ppt

.******@  DecisionvariablesinanLPmodelareallowedtohaveanyvalues,includingnonintegervalues,.,:realmofintegerprogramming!!!RevisitingtheTBAAirlinesProblem,orstartmovingintothenationalmarketbypurchasingsomelargeairplanes,:annualprofit?DatafortheTBAAirlinesProblemSmallAirplaneLargeAirplaneCapitalannualprofitperairplane$1million$5millionPurchasecostperairplane5million50million$100millionMaximumpurchasequantity2—LinearProgrammingFormulationLet S=Numberofsmallairplanestopurchase L=NumberoflargeairplanestopurchaseMaximizeProfit=S+5L($millions)subjectto CapitalAvailable: 5S+50L≤100($millions) MaxSmallPlanes: S≤2and S≥0,L≥:Decisionvariablesinalinearprogrammingmodelareallowedtohaveanyvalues,includingfractionalvalues,,, S=Numberofsmallairplanestopurchase L=NumberoflargeairplanestopurchaseMaximizeProfit=S+5L($millions)subjectto CapitalAvailable: 5S+50L≤100($millions) MaxSmallPlanes: S≤2and S≥0,L≥0 S,