数据、模型与决策(运筹学)课后习题和案例答案017s

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1、CDSUPPLEMENTTOCHAPTER17MOREABOUTTHESIMPLEXMETHODReviewQuestions17s.1-1No.17s.1-2Theadjacentcornerpointsthatarebetterthanthecurrentcornerpointarecandidatestobethenextone.17s.1-3Thebestadjacentcornerpointcriteriaandbestrateofimprovementcriteria.17s.1-4Thesimplexmethodstartsbyselec

2、tingsomecornerpointastheinitialcornerpoint.17s.1-5Ifnoneoftheadjacentcornerpointsarebetter(asmeasuredbythevalueoftheobjectivefunction)thanthecurrentcornerpoint,thenthecurrentcornerpointisanoptimalsolution.17s.1-6Choosethebestadjacentcornerpoint.17s.1-7Choosethenextcornerpointbyp

3、ickingtheadjacentcornerpointhasthelowestobjectivefunctionvalueratherthanhighestwhengettingstarted.Theremayonlybeoneadjacentcornerpointifthefeasibleregionisunbounded.17s.2-1Itisanalagoustostandinginthemiddleofaroomandlookingtowardonecornerwheretwowallsandthefloormeet.17s.2-2There

4、arethree(atmost)adjacentcornerpoints.17s.2-3Yes.17s.2-4Withthreedecisionvariables,theconstraintboundariesareplanes.17s.2-5Asystemofnvariablesandnequationsmustbesolved.17s.3-1Thenamederivesfromthefactthattheslackvariablefora≤constraintrepresentstheslack(gap)betweenthetwosidesofth

5、einequality.17s.3-2Anonnegativeslackvariableimpliesthattheleft-handsideisnotlargerthantheright-handside.17s.3-3FortheWyndorproblem,theslackvariablesrepresentunusedproductiontimesinthevariousplants.17s.3-4Itismuchsimplerforanalgebraicproceduretodealwithequationsthanwithinequaliti

6、es.17s.3-5Anonbasicvariablehasavalueofzero.17s.3-6Abasicfeasiblesolutionissimplyacornerpointthathasbeenaugmentedbyincludingthevaluesoftheslackvariables.17s.3-7Asurplusvariablegivestheamountbywhichtheleft-handsideofa≥constraintexceedstheright-handside.CD17s-1817s.4-1(1)Determinet

7、heenteringbasicvariable;(2) determinetheleavingbasicvariable;(3) Solveforthenewbasicfeasiblesolution17s.4-2Theenteringbasicvariableisthecurrentnonbasicvariablethatshouldbecomeabasicvariableforthenextbasicfeasiblesolution.Amongthenonbasicvariableswithanegativecoefficientinequatio

8、n0,choosetheonewhosecoefficienthasthelargestabs