数据模型与决策运筹学课后习题和案例答案017Word格式.docx
- 文档编号:21288131
- 上传时间:2023-01-29
- 格式:DOCX
- 页数:34
- 大小:1.25MB
数据模型与决策运筹学课后习题和案例答案017Word格式.docx
《数据模型与决策运筹学课后习题和案例答案017Word格式.docx》由会员分享,可在线阅读,更多相关《数据模型与决策运筹学课后习题和案例答案017Word格式.docx(34页珍藏版)》请在冰豆网上搜索。
17.3-1Thesimplexmethodfocusessolelyonsolutionsthatarecornerpoints.
17.3-2Eachiterationofthesimplexmethodconsistsofaprescribedseriesofstepsformovingfromthecurrentcornerpointtoanewcornerpoint.
17.3-3Managementsciencealgorithmstypicallyareiterativealgorithms.
17.3-4Wheneverpossible,theinitializationstepofthesimplexmethodchoosestheorigin(0,0)tobetheinitialcornerpointtobeexamined.
17.3-5Whenthesimplexmethodfinishesexaminingacornerpointitthengathersinformationabouttheadjacentcornerpoints.Itidentifiestheratesofimprovementintheobjectivefunctionalongtheedgesthatleadtotheadjacentcornerpoints.
17.3-6Theoptimalitytestconsistssimplyofcheckingwhetheranyoftheedgesgiveapositiverateofimprovementintheobjectivefunction.Ifnonedo,thenthecurrentpointisoptimal.
17.4-1Aproblemwithseveralthousandfunctionalconstraintsandmanythousanddecisionvariablesisnotconsideredunusuallylargeforafastcomputer.
17.4-2Thesoftwarepackageneedstohelpformulate,input,andmodifythemodel.Inadditionitshouldanalyzesolutionsfromthemodelandpresentresultsinthelanguageofmanagement.
17.5-1NarendaKarmarkar.
17.5-2Today,themorepowerfulsoftwarepackagesincludeatleastoneinterior-pointalgorithmalongwiththesimplexmethod.
17.5-3Interior-pointalgorithmsshootthroughtheinteriorofthefeasibleregiontowardanoptimalsolutioninsteadoftakingalessdirectpatharoundtheboundaryofthefeasibleregion.
17.5-4Thecomputertimeperiterationforaninterior-pointalgorithmismanytimeslongerthanforthesimplexmethod.
17.5-5Forfairlysmallproblems,thenumberofiterationsneededbyaninterior-pointalgorithmandthesimplexmethodtendtobesomewhatcomparable.Forlargeproblems,interior-pointalgorithmsdonotneedmanymoreiterationswhilethesimplexmethoddoes.Thereasonforthelargedifferenceisthedifferenceinthepathsfollowed.
17.5-6Thesimplexmethodisverywellsuitedforwhat-ifanalysiswhiletheinterior-pointapproachcurrentlyhaslimitedcapabilityinthisarea.
17.5-7Thelimitedcapabilityforperformingwhat-ifanalysiscanbeovercomebyswitchingovertothesimplexmethod.
17.5-8Switchingoverbeginsbyidentifyingacornerpointthatisveryclosetothefinaltrialsolution.
Problems
17.1
CornerPoint(A1,A2)
Profit=$1,000A1+$2,000A2
(0,0)
$0
(8,0)
$8,000
(6,4)
$14,000
(5,5)
$15,000
(0,6.667)
$13,333
OptimalSolution:
(A1,A2)=(5,5)andProfit=$15,000.
17.2
CornerPoint(TV,PM)
Cost=TV+2PM
(0,9)
$18
(4,3)
$12
(8,3)
$14
(TV,PM)=(4,3)andCost=$12.
17.3a&
d)
b&
e)OptimalSolution:
(x1,x2)=(3,3)andProfit=$150.
CornerPoints:
(0,0),(4.5,0),(3,3),(1.667,4),and(0,4).
c)
CornerPoint(x1,x2)
Profit=$30x1+$20x2
(4.5,0)
$135
(3,3)
$150
(1.667,4)
$130
(0,4)
$80
(x1,x2)=(3,3)andProfit=$150.
17.4a&
d)
(x1,x2)=(3,5)andProfit=$1,900.
(0,0),(6,0),(3,5),(1.5,6),and(0,6).
Profit=$300x1+$200x2
(6,0)
$1800
(3,5)
$1900
(1.5,6)
$1650
(0,6)
$1200
17.5a)ObjectiveFunction:
Profit=$400x1+$400x2
(x1,x2)=(2,6)andProfit=$3,200
ObjectiveFunction:
Profit=$500x1+$300x2
(x1,x2)=(4,3)andProfit=$2,900
Profit=$300x1–$100x2
(x1,x2)=(4,0)andProfit=$1,200
Profit=–$100x1+$500x2
(x1,x2)=(0,6)andProfit=$3,000
ObjectiveFunction:
Profit=–$100x1–$100x2
(x1,x2)=(0,0)andProfit=$0
b)ObjectiveFunction:
CornerPoint(x1,x2)
Profit=$400x1+$400x2
$2,400
(4,0)
$1,600
(2,6)
$3,200
$2,800
Profit=$500x1+$300x2
$1,800
$2,000
$2,800
$2,900
(x1,x2)=(4,0)andProfit=$1,200
Profit=$300x1-$100x2
-$600
$1,200
$0
$900
(x1,x2)=(0,6)andProfit=$3,000
Profit=-$100x1+$500x2
$3,000
-$400
$1,100
Profit=–$100x1–$100x2
–$600
–$400
–$800
–$700
17.6a)True.(Example:
MaximizeProfit=–x1+4x2)
b)True.(Example:
MaximizeProfit=–x1+3x2)
c)False.(Example:
MaximizeProfit=–x1–x2)
17.7a)x1≤6
x2≤3
–x1+3x2≤6
b)
Unit
Profit
Product1
Product2
ObjectiveFunction
MultipleOptimalSolutions
–$1
$3
Profit=–x1+3x2
linesegmentbetween(0,2)&
(3,3)
$1
Profit=x2
linesegmentbetween(3,3)&
(6,3)
Profit=x1
linesegmentbetween(6,3)&
(6,0)
Profit=–x2
linesegmentbetween(0,0)&
Profit=–x1
(0,2)
c)ObjectiveFunction:
Profit=–x1+5x2
(x1,x2)=(3,3)andProfit=$12
Profit=–x1+5x2
(0,2)
$10
(6,3)
$9
-$6
d)ObjectiveFunction:
Profit=–x1+2x2
(x1,x2)=(0,2)andProfit=$4
CornerPoint
Profit=-x1+2x2
$4
17.8a)
b)ThesensitivityreportindicatesthattheproblemhasotheroptimalsolutionsbecausetheallowableincreaseofActivity1andtheallowabledecreaseofActivity2are0.Analternativeoptimalsolutionisshownbelow(obtainedbyadjustingtheunitprofitforActivity2to29.99).
c)Theotheroptimalsolutionswillbelocatedonthelinesegmentconnectingthetwooptimalsolutionsfoundinpartsaandb.
d)OptimalSolution:
(x1,x2)=(2.857,1.429),(1.25,2.5)andallpointsontheconnectingline.Profit=$100million.
17.9a)
b)ThesensitivityreportindicatesthattheproblemhasotheroptimalsolutionsbecausetheallowabledecreaseofActivity1andtheallowableincreaseofActivity2are0.Analternativeoptimalsolutionisshownbelow(obtainedbyadjustingtheprofitforactivity2to$300.01).
c)Theotheroptimalsolutionswillbelocatedonthelinesegmentconnectingthetwooptimalsolutionsfoundinpartsa)andb).
(x1,x2)=(15,15),(2.5,35.833)andallpointsontheconnectingline.Profit=$12,000.
17.10FeasibleRegion:
Case1(c2=0):
Ifc1>
0,theobjectiveincreasesasx1increases,sotheoptimalsolutionis(x1,x2)=(5.5,0).
Ifc2<
0,theoppositeistrue,sotheoptimalsolutionis(x1,x2)=(0,0),(0,1)andtheconnectingline.
(Noteifc1=0,everyfeasiblepointgivestheoptimalsolution,as0x1+0x2=0).
Case2(c2>
0)
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 数据模型 决策 运筹学 课后 习题 案例 答案 017