数据、模型与决策(运筹学)课后习题和案例答案017

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1、CDCHAPTER17SOLUTIONCONCEPTSFORLINEARPROGRAMMINGReviewQuestions17.1-1Acomerpointisapointthatliesatacornerofthefeasibleregion.17.1-2Thecomerpointwiththebestvalueoftheobjectivefunctionistheoptimalsolution.17.1-3Thesimplexmethodhasawayofquicklygettingtothebestcomerpoin

2、tanddetectingthatthispointisoptimal,soitstopswithoutneedingtoevaluatetherestofthecornerpoints.17.1-4No.Itcanhaveoneoptimalsolution,aninfinitenumberofoptimalsolutions,ornooptimalsolution.17.1-5Yes,andeverypointofthelinesegmentbetweenthesetwocomerpointswillbeanoptima

3、lsolution・17.1-6Theconstraintsofalinearprogrammingproblemcanbesorestrictivethatitisimpossibleforasolutiontosatisfyalloftheconstraintssimultaneously.17.1-7Ifsomenecessaryconstraintwerenotincludedinthelinearprogrammingmodel,itispossibletohavenolimitonthebestobjective

4、functionvalue・17.2-1Thebestcomerpointisalwaysanoptimalsolution.17.2-2Thebigadvantageofsearchingforanoptimalsolutionsimplybyfindingthebestcomerpointisthatittremendouslyreducesthenumberofsolutionsthatneedtobeconsidered・17.2-3Whenthesimplexmethodisreadytomovefromthecu

5、rrentcomerpointtothenextone,theadjacentcornerpointsarecandidatestobethenextone.17.2-4Ifnoneoftheadjacentcomerpointsarebetterthanthecurrentcomerpoint,thenthecurrentcornerpointisanoptimalsolution.17.2-5Ifthesimultaneoussolutionofasetofconstraintboundaryequationsisfea

6、siblethenthatsolutionisacornerpoint.17.2・6Twocomerpointsareadjacenttoeachotheriftheyshareallbutoneofthesameconstraintboundaries.17.2・7Thesimplexmethodexaminescornerpointsinanordersuchthateachoneisadjacenttotheprecedingone.Thisgreatlystreamlinesthealgebra.17.2-8Apro

7、blemwith20decisionvariableand30functionalconstraintsmighthavemorethanabillioncomerpoints.17.2-9Thesimplexmethodcansolveproblemsthattheenumeration-of^corner-pointsmethodcannotbecauseitisabletoreachandidentifytheoptimalcornerpointforalargeproblemafterexaminingonlyasm

8、allfractionofallthecomerpoints.17.1-1Thesimplexmethodfocusessolelyonsolutionsthatarecomerpoints.17・3・2Eachiterationofthesimplexmethodconsistsofap