搜索
CD17s-1CDSUPPLEMENTTOCHAPTER17MOREABOUTTHESIMPLEXMETHODReviewQuestions17s.1-1No.17s.1-2Theadjacentcornerpointsthatarebetterthanthecurrentcornerpointarecandidatestobethenextone.17s.1-3Thebestadjacentcornerpointcriteriaandbestrateofimprovementcriteria.17s.1-4Thesimplexmethodstartsbyselectingsomecornerpointastheinitialcornerpoint.17s.1-5Ifnoneoftheadjacentcornerpointsarebetter(asmeasuredbythevalueoftheobjectivefunction)thanthecurrentcornerpoint,thenthecurrentcornerpointisanoptimalsolution.17s.1-6Choosethebestadjacentcornerpoint.17s.1-7Choosethenextcornerpointbypickingtheadjacentcornerpointhasthelowestobjectivefunctionvalueratherthanhighestwhengettingstarted.Theremayonlybeoneadjacentcornerpointifthefeasibleregionisunbounded.17s.2-1Itisanalagoustostandinginthemiddleofaroomandlookingtowardonecornerwheretwowallsandthefloormeet.17s.2-2Therearethree(atmost)adjacentcornerpoints.17s.2-3Yes.17s.2-4Withthreedecisionvariables,theconstraintboundariesareplanes.17s.2-5Asystemofnvariablesandnequationsmustbesolved.17s.3-1Thenamederivesfromthefactthattheslackvariablefora≤constraintrepresentstheslack(gap)betweenthetwosidesoftheinequality.17s.3-2Anonnegativeslackvariableimpliesthattheleft-handsideisnotlargerthantheright-handside.17s.3-3FortheWyndorproblem,theslackvariablesrepresentunusedproductiontimesinthevariousplants.17s.3-4Itismuchsimplerforanalgebraicproceduretodealwithequationsthanwithinequalities.17s.3-5Anonbasicvariablehasavalueofzero.17s.3-6Abasicfeasiblesolutionissimplyacornerpointthathasbeenaugmentedbyincludingthevaluesoftheslackvariables.CD17s-217s.3-7Asurplusvariablegivestheamountbywhichtheleft-handsideofa≥constraintexceedstheright-handside.17s.4-1(1)Determinetheenteringbasicvariable;(2)determinetheleavingbasicvariable;(3)Solveforthenewbasicfeasiblesolution17s.4-2Theenteringbasicvariableisthecurrentnonbasicvariablethatshouldbecomeabasicvariableforthenextbasicfeasiblesolution.Amongthenonbasicvariableswithanegativecoefficientinequation0,choosetheonewhosecoefficienthasthelargestabsolutevaluetobetheenteringbasicvariable.17s.4-3Theleavingbasicvariableisthecurrentbasicvariablethatshouldbecomeanonbasicvariableforthenextbasicfeasiblesolution.Foreachequationthathasastrictlypositivecoefficient(neitherzeronornegative)fortheenteringbasicvariable,taketheratiooftheright-handsidetothiscoefficient.Identifytheequationthathastheminimumratio,andselectthebasicvariableinthisequationtobetheleavingbasicvariable.17s.4-4Theinitializationstepsetsuptostarttheiterationsandfindstheinitialbasicfeasiblesolution.17s.4-5Examinethecurrentequation0.Ifnoneofthenonbasicvariableshaveanegativecoefficient,thenthecurrentbasicfeasiblesolutionisoptimal.17s.4-6(1)Equation0doesnotcontainanybasicvariables;(2)eachoftheotherequationscontainsexactlyonebasicvariable;(3)anequation’sonebasicvariablehasacoefficientof1;(4)anequation’sonebasicvariabledoesnotappearinnanyotherequation.17s.4-7Thetabularformperformsexactlythesamestepsasthealgebraicform,butrecordstheinformationmorecompactly.CD17s-3Problems17s.1GettingStarted:Select(0,0)astheinitialcornerpoint.CheckingforOptimality:Both(0,3)and(3,0)havebetterobjectivefunctionvalues(Z=6and9,respectively),so(0,0)isnotoptimal.MovingOn:(3,0)isthebestadjacentcornerpoint,somoveto(3,0).CheckingforOptimality:(2,2)hasabetterobjectivefunctionvalue(Z=10),so(3,0)isnotoptimal.MovingOn:Movefrom(3,0)to(2,2).CheckingforOptimality:(0,3)haslowerobjectivefunctionvalues(Z=6),so(2,2)isoptimal.CD17s-417s.2GettingStarted:Select(0,0)astheinitialcornerpoint.CheckingforOptimality:Both(0,2.667)and(4,0)havebetterobjectivefunctionvalues(Z=5.333and4,respectively),so(0,0)isnotoptimal.MovingOn:(0,2.667)isthebestadjacentcornerpoint,somoveto(0,2.667).CheckingforOptimality:(2,2)hasabetterobjectivefunctionvalue(Z=6),so(0,2.667)isnotoptimal.MovingOn:Movefrom(0,2.667)to(2,2).CheckingforOptimality:(4,0)hasalowerobjectivefunctionvalues(Z=4),so(2,2)isoptimal.CD17s-517s.3GettingStarted:Select(0,0)astheinitialcornerpoint.CheckingforOptimality:Both(0,5)and(4,0)havebetterobjectivefunctionvalues(Z=10and12,respectively),so(0,0)isnotoptimal.MovingOn:(4,0)isthebestadjacentcornerpoint,somoveto(4,0).CheckingforOptimality:(4,2)hasabetterobjectivefunctionvalue(Z=16),so(4,0)isnotoptimal.MovingOn:Movefrom(4,0)to(4,2).CheckingforOptimality:(3,4)hasabetterobjectivefunctionvalue(Z=17),so(4,2)isnotoptimal.MovingOn:Movefrom(4,2)to(3,4).CheckingforOptimality:(0,5)hasalowerobjectivefunctionvalues(Z=10),so(3,4)isoptimal.CD17s-617s.4a)GettingStarted:Select(0,0)astheinitialcornerpoint.CheckingforOptimality:Both(2,0)and(0,5)havebetterobjectivefunctionvalues(Z=4and5,respectively),so(0,0)isnotoptimal.MovingOn:(0,5)isthebestadjacentcornerpoint,somoveto(0,5).CheckingforOptimality:(2,5)hasabetterobjectivefunctionvalue(Z=9),so(0,5)isnotoptimal.MovingOn:Movefrom(0,5)to(2,5).CheckingforOptimality:(2,0)hasalowerobjectivefunctionvalues(Z=4),so(2,5)isoptimal.b)GettingStarted:Select(0,0)astheinitialcornerpoint.CheckingforOptimality:Movingtowardeither(2,0)or(0,5)improvestheobjectivefunctionvalue,so(0,0)