英文版运筹学期末试卷

1XXXX学年第X学期《运筹学》期末试卷ClassIDNumberNameScoreI.True/False(1)Abalancedtransportationproblemhasthesamenumberofsupplypointsasdemandpoints.(2)InthesearchforanoptimalsolutionofanLPproblem,onlyvertexesoffeasibleregionareneededtobeconsidered.(3)Thesteppingstonemethodisusedbecausethetransportationproblemcannotbesolvedviathesimplexmethod.(4)LinearProgrammingcanbeemployedtosolveproblemswithsingleobjective.(5)Ifaresourceisnotfinishedout,thenitsshadowpricemustbepositive.(6)Thefirststepinapplyingthesimplexmethodistotransformallinequalityconstraintsintoequalityconstraintsbyaddingslackvariablesandsubtractingsurplusvariables.(7)Theoptimalvalueoftheprimalobjectivefunctionisequaltotheoptimalvalueofthedualobjectivefunction.(8)Ifaconstraintisin“≥”forminLPproblem,thenartificialvariableisnecessary.(9)ThatthefeasibleregionofLPisnotemptymeans:(A)itincludestheoriginX=(0,0,…,0);(B)itisbounded;(C)itisunbounded;(D)itisconvex.(A,B,C,D)(10)Boththeprimalanddualproblemsareoffeasiblesolution,thenmaybe(A)anoptimalsolutionisavailableforprimalproblem,buttheoptimalsolutionisnotavailablefordualproblem;(B)atleastoneproblemisunbounded;(C)anoptimalsolutionisavailableforoneproblem,andtheotherproblemisofunboundedsolution;(D)boththeprimalanddualproblemsmightbeofoptimalsolution.(A,B,C,D)2II.Tosolvetheproblemsbelow:(1)Min.w=14X1+20X2s.t.X1+4X2≥4X1+5X2≥22X1+3X2≥7X1,X2≥0Pleasefindouttheoptimalsolutionsforboththisproblemanditsdual.(2)TheobjectivefunctionofanLPisMax.Z=5X1+6X2+8X3.ThisLPisoftwoconstraints(resources#1and#2respectively)with“≤”form.Belowisaprocessingstepbyusingsimplexmethod.2551/2-1/23/2-1/2101/2-3/201a)Tocompletethistable;b)Isthistableoptimal?If“yes”,thendoc);if“no”,thenfindouttheoptimaltable.c)Towriteouttheoptimalsolutionandobjectivevalue.d)Towriteouttheshadowpricesofresources#1and#2,anddescribethesignificances.3III.TofindtheshortestpathanditslengthfromAtoE:7B1C11644D1M+1236A4B22C2E3434413D2B33C33MisthelastplaceofyourIDnumber.VI.Tosolvethetransportationproblembelow:D1D2D3supplyS1M+11812S224114S33674demand91011MisthelastplaceofyourIDnumber.4IV.AfactoryisgoingtoproduceProductsI,IIandIIIbyusingrawmaterialsA,BandC.Therelateddataisshownbelow:RawmaterialIIIIIIRawmaterialavailableABC211123221200(kg)500(kg)600(kg)Profit($)413a)Pleasearrangeproductionplantomaketheprofitmaximization.b)IfonemorekgofrawmaterialAisavailable,howmuchthetotalprofitwillbeincreased?c)ThemarketpriceforrawmaterialBis$1.2.Willthefactorybuyitorsellit?Why?d)WhatistheallowedrangeforrawmaterialsA,BandCrespectively?e)WhatistheallowedrangefortheprofitofproductII?