運(yùn)籌學(xué)第五版課后答案,運(yùn)籌作業(yè)

1、47頁(yè)1.1b用圖解法找不到滿(mǎn)足所有約束條件的公共范圍，所以該問(wèn)題無(wú)可行解47頁(yè)1.1d1.2（b）約束方程的系數(shù)矩陣A=P1P2P3P4基基解是否可行解目標(biāo)函數(shù)值X1X2X3X4P1P2-411/20否P1P32/5011/5是43/5P1P4-1/311/600否P2P301/220是5P2P40-1/202否P3P40011是5最優(yōu)解A=(01/220)T和(0011)T49頁(yè)13題設(shè)Xij為第i月租j個(gè)月的面積minz=2800 x11+2800 x21+2800 x31+2800 x41+4500 x12+4500 x22+4500 x32+6000 x13+6000 x23+730

2、0 x14s.t.x11+x12+x13+x14$15x12+x13+x14+x21+x22+x23$10 x13+x14+x22+x23+x31+x32$20 x14+x23+x32+x41$12XijMO用excel求解為：用LINDO求解:LPOPTIMUMFOUNDATSTEP3OBJECTIVEFUNCTIONVALUE1)1)VARIABLEZX11118400.0VALUE0.0000003.000000REDUCEDCOST1.0000000.000000X210.0000002800.000000X318.0000000.000000X410.0000001100.00000

3、0X120.0000001700.000000X220.0000001700.000000X320.0000000.000000X130.000000400.000000X230.0000001500.000000X1412.0000000.000000NO.ITERATIONS二3NO.ITERATIONS二3FileEfiitSolveReportsWindowHelpROWSLACKORSURPLUSDUALPRICES2)0.000000-2800.0000003)2.0000000.0000004)0.000000-2800.0000005)0.0000001700.000000門(mén)血

4、吒日耳Ll啟知區(qū)環(huán)創(chuàng)胃口百、口曰申甩廿師適ReportsWbdcxwLP0PIIMUMFOUNDATSTEP&OBJECTIVEFUNCTIONVALUEVARIABLEZKIVARIABLEZKI畑UX12X22K32K13X23mYALLTOL0000003.000000aooooro&:mooo.000000o.ooooooo.oooooo0.0000000.woow0.OOOOtK12.000000EEDUCEDCOSTLODOOOOQ.DMMMO2800.OWKMO0.OWXMOLLOO.0WMM01700.OOOOOO1700.OOOOOO0.OOOOOO400.0000001-i

5、OO.OWXMO0.ODOOOO小“3)4小“3)45DIALPRICES-2800.DDOOOO0.0WXM0-2300.000000-1700.ODOOOO0.OOOQQOOOOOOQ00000000000000NO.ITERATION滬宰vuncitlednilnz2SOOx11+2300 x21+2SOOU31-2800 x41+4500 x12+4500 x22-45003432-5000 x13+&000 x23+7300 x14s.t”xll+zl2-xl3+e1415x12-hc13-x14i-x2L+k22+x2J1013+s14+522+x23+K31t8322014-ht

6、23-x32+x412eridl答若使所費(fèi)租借費(fèi)用最小，需第一個(gè)月租一個(gè)月租期300平方米，租四個(gè)月租期1200平方米，第三個(gè)月租一個(gè)月租期800平方米，50頁(yè)14題設(shè)al,a2,a3,a4,a5分別為在A1,A2,B1,B2,B3加工的丨產(chǎn)品數(shù)量，bl,b2,b3分別為在A1,A2,B1加工的1丨產(chǎn)品數(shù)量，cl為在A2,B2上加工的III產(chǎn)品數(shù)量。則目標(biāo)函數(shù)為maxz=(1.25-0.25)(a1+a2+a3)+(2-0.35)b3+(2.8-0.5)c1-0.05(a1+b1)-0.03(a2+b2+c1)-0.06(a3+b3)-0.11(a4+c1)-0.05a5=0.95a1+0.9

7、7a2+0.94a3+1.5b3+2.1c1-0.05b1-0.11a4-0.05a5s.t.r5a1+10b1W60007a2+b2+12c1W100006a3+8a3W4000)4a4+11c1W70007a5W4000a1+a2-a3-a4-a5=0b1+b2-b3=0al,a2,a3,a4,a5,bl,b2,b3,c1$0用lindo求解得：LPOPTIMUMFOUNDATSTEP6OBJECTIVEFUNCTIONVALUE1)16342.29VARIABLEVALUEREDUCEDCOSTA11200.0000000.000000A20.0000009.640000A3285.71

8、42940.000000B310000.0000000.000000C10.00000015.900000B10.0000000.230000A4342.8571470.000000A5571.4285890.000000B210000.0000000.0000002)0.0000000.1680003)0.0000001.5000004)0.0000000.0750005)5628.5712890.0000006)0.0000000.0085717)0.0000000.1100008)0.000000-1.500000ROWSLACKORSURPLUSDUALPRICESNO.ITERATI

9、ONS二6計(jì)算lindo截屏FdaE-dltiaNaFU-porKWndawH-s-pFdaE-dltiaNaFU-porKWndawH-s-pD也耳日I題1-丨|電劃El張蜃創(chuàng)回I0IBI宙豐盤(pán)曜囲說(shuō)pixrs冊(cè)IPOPT1ML31POUNDATSTEPIPOPT1ML31POUNDATSTEP1)1342,29VARIABLE1)1342,29VARIABLEVALUEREDCCEDCOSTAl1200.0000000.000000A20-oooooo9MOOOOA3285.714294aOQODOOB31OG00.OOOOWaooooooCl0.00000015.900000El0-M0

10、0OT0.230000A4342.857147aowowA57L4285S9aooooooB2：!0000.000000o.ooooooOBJECTIVEFLyCTIOXVALLE國(guó)runlitlcdrhiC.S5e140.&?a2-G.94a3-l.5hd+2lc-.D6bl-O.Ila4-Q.O5a55alHQbl=flOOO7a24j2+12eJ=lOOOO6a3+-03-=4OiOia4+llcl=07h5=4000&l-i2-a3-a-fi5=Obl-b2-b3=0end|RWSLACKOKSURPLUSDCALFUICES2)0.OOOftOO0.l&SDOO3)0.OOO&OOL

11、5H)0004)0,OOOWWa0750005)502S-571289aOQODOO笳0.OOOOWaOOS5717)0.OOOGOO0.110000a)D.OOOOOT-1.aMOOM.ITERATION62.1a:對(duì)偶問(wèn)題為：maxz=2y1+3y2+5y3s.t.y1+2y2+y3W23y3+y2+4y3W24y1+3y2+3y3=4y10,y2W0,y3無(wú)約束因?yàn)樵瓎?wèn)題的對(duì)偶問(wèn)題的對(duì)偶問(wèn)題仍是原問(wèn)題，因此本問(wèn)題的對(duì)偶問(wèn)題的對(duì)偶問(wèn)題為：minz=2x1+2x2+4x3s.t.lx1+3x2+4x3M22x1+x2+3x3W3x1+4x2+3x3=51頁(yè)2.12、x1,x2$0,x3無(wú)約束

12、1頁(yè)2.12設(shè)x1,x2,x3分別為A,B,C產(chǎn)品數(shù)量maxz=3x1+x2+4x3s.t.6x1+3x2+5x3W453x1+4x2+5x3W30 x1,x2,x3$0用lomdo求解為L(zhǎng)POPTIMUMFOUNDATSTEP2OBJECTIVEFUNCTIONVALUE27.00000VARIABLEX1X2VARIABLEX1X2X35.0000000.0000000.0000002.0000003.0000000.000000X1,X2,X30.0000000.000000ROWSLACKORSURPLUSDUALPRICESROWSLACKORSURPLUSDUALPRICES0.0

13、000000.2000000.0000000.6000000.0000000.000000NO.ITERATIONS二2瞻ReportsWindowLPOPTimfFOUNDATSTEP2OBJECTIVEFUNCTIONVALUEREDUCEDCOST0.0000002.0000000.0000000.000000瑙pax3xl+x2-4x3s.t.6xl+3x2+5x3=453xl-4x2+5x3=0elic|1)VARIABLEXIX2X3XI,X2,X327.00000VALLE：5.0000000.0000003.0000000.000000ROWSLACKORSURPLUSDUAL

14、PRICES2)0.0000000.2000003)0.0000000.6000004)0.0000000.000000NO.ITERATIONS:2最大生產(chǎn)計(jì)劃為A生產(chǎn)5個(gè)單位，C生產(chǎn)3個(gè)單位b)LPOPTIMUMFOUNDATSTEP2OBJECTIVEFUNCTIONVALUE1)27.00000VARIABLEVALUEREDUCEDCOSTX15.0000000.000000X20.0000002.000000X33.0000000.000000X1,X2,X30.0000000.000000DUALPRICES0.200000DUALPRICES0.2000000.6000000.

15、0000000.0000000.0000000.000000NO.ITERATIONS=2RANGESINWHICHTHEBASISISUNCHANGED:OBJCOEFFICIENTRANGESVARIABLECURRENTALLOWABLEALLOWABLECOEFINCREASEDECREASEX13.0000001.8000000.600000X21.0000002.000000INFINITYX34.0000001.0000001.500000X1,X2,X30.0000000.000000INFINITYRIGHTHANDSIDERANGESROWCURRENTALLOWABLEA

16、LLOWABLERHSINCREASEDECREASE245.00000015.00000015.000000330.00000015.0000007.50000040.0000000.000000INFINITY隅ReportsWindu-Ai7.P-rrTKTiAT=FRTFi-TTV?FFlTTn-1?廣卞127COIOIVARIABLEVALUEREDUCEDCCS!KI5OOOOOOi：L000000S3O.OOOOOO2.OOODaDK33.000000IJ.IJLIIJLIOOK1.T2jnDOOOOOO0.OQODQDSLACKORSURPLUSo.uouooo00000000

17、.000000DUlPRICES0.200DOO0.6O0D0Dn.nnnnnn闔max3瓦1十x24x3s.1,6xl-3x2+5x3=453xl-4x2+5x3=0encllNOITERATIONS=RANGESINUH1CHTHEBi5ISISITNCONGED:OEJCOEFFICIENTRANGESVAE1ABLEZ11213KI.2.S3CUERENTCOEF.OijQuOul.OOUOUO000000a.ooooooAL10VAELEIHCE?EASE1.sooooo2JJIJOOIJO1riuooooD.ononooALLOVAELEDECREASE0jz-ODODOINFIH

18、ITY1SLiOODOINFINITEE?OWCURRENTFIGHTHANDSIDERANGES1L1UVABLEALLOUABLERHSIHCE?EASEDECREASE2AS.000000L5.ononon15JjnDODO:90.00000015.0000007.50D0DQ4aoooooo.OOQOQOTHFINITV可知A產(chǎn)品的利潤(rùn)變化范圍【6.&2.4】，上述計(jì)劃不變。C)設(shè)x4為產(chǎn)品D的數(shù)量maxz=3x1+x2+4x3+3x4s.t.*6x1+3x2+5x3+8x4W45v3x1+4x2+5x3+2x430、x1,x2,x3,x4$0用lomdo求解為L(zhǎng)POPTIMUMFOU

19、NDATSTEP0OBJECTIVEFUNCTIONVALUE1)27.50000VARIABLEVALUEREDUCEDCOSTX10.0000000.100000X20.0000001.966667X35.0000000.000000X42.5000000.000000ROWSLACKORSURPLUSDUALPRICES0.0000000.2333330.0000000.566667NO.ITERATIONS=0LPOPTIMUMFOUNDATSTEP2OBJECTIF12CTIOVALUE1)汀.刊LPOPTIMUMFOUNDATSTEP2OBJECTIF12CTIOVALUE1)汀.

20、刊000VARIABLEXIX2K3X4VAL7EREDUCEDCOST0.000000D1000000.0000001.9666S75.OOOOOO0.OOOOOO2.5000000.0000DOROWSLCKORSURPLJSDUALPRICES2)o.ooooaa0.2333333)0.0000000.5666&74)0.0000000.000000砧0.0000000.0000&D6)5.0000000.000000D2.5000000.000000ND.iTEEtAllOXS:2圍max3x1-x2+4x3+3x4s.t.6x13x2+5x3+8x4-453x1-4x2+5x3+2x

21、40 x2-0 x3-0 x4-0end安排生產(chǎn)D有利，新最有生產(chǎn)計(jì)劃為x1=x2=0,x3=5,x4=2.5，利潤(rùn)為27.5d)maxz二3x1+x2+4x3-0.4ys.t.廠(chǎng)6x1+3x2+5x345y3x1+4x2+5x3-yW30 x1,x2,x3,y$0用lomdo求解為L(zhǎng)POPTIMUMFOUNDATSTEP0OBJECTIVEFUNCTIONVALUE1)30.00000VARIABLEVALUEREDUCEDCOSTX10.0000000.600000X20.0000001.800000X39.0000000.000000Y15.0000000.000000ROWSLACKO

22、RSURPLUSDUALPRICES0.0000000.4000000.0000000.4000004.1喟ReportscVindcwLFOPTIMUMFOLXDATSTEP0max3xl-x2+4x3-0-ly5.t-6xl-3x2-jx3=43OBJECTIVEFIBCTIONVALUEVARIABLEVALUEREDUCEDCOSTXIo.oooooo0”600000X20.0000001,800000X39.0000004.1喟ReportscVindcwLFOPTIMUMFOLXDATSTEP0max3xl-x2+4x3-0-ly5.t-6xl-3x2-jx3=43OBJECTIV

23、EFIBCTIONVALUEVARIABLEVALUEREDUCEDCOSTXIo.oooooo0”600000X20.0000001,800000X39.0000000.000000Y15.0000000”0000001)30.00000ROWSLACKORSURPLUSDUJ.PRICES?)0.OOOOOO0.4000000.OOOOOO0.4000000.OOOOOO0.0000000.OOOOOO0.oooooo9.0000000.OOOOOO15.0000000.OOOOOOXO.ITERATIONS0可知購(gòu)進(jìn)原材料15個(gè)單位為宜。3xl-4x2-5x3-y-0 x2-0 x3=0

24、y0end|a)設(shè)yi二1第i組條件起作用第i組條件不起作用x1+x2W2-(1-y1)M2x1+3x2$5+(1-y2)My1+y2=1y1,y2=0或1M一充分大正數(shù)b)設(shè)yib)設(shè)yi二1第i組條件起作用.0第i組條件不起作用廠(chǎng)x=OylLx=3y2x=5y2x=7y4y1+y2+y3+y4=1y1,y2,y3,y4=0或1設(shè)yi二1為假定取值$500為假定取值x=0 x=0y1Ix$50一(1-y2)Mfy1+y2=1Ly1,y2=0或1D設(shè)yi二1第i組條件起作用i=1,2則i=1,2則0第i=1,2則i=1,2則x1W2+(1y1)Mx2$1-(1-y1)MSx2W4+(1-y2)

25、My1+y2=1jy1,y2=0或1設(shè)yi二”1第i組條件起作用0第i組條件不起作用rx1+x25-(1-y1)Mx1W2-(1-y2)Mx3$2+(1-y3)Mx3+x4$6+(1y4)My1+y2+y3+y4$2Ly1,y2,y3,y4=1或04.2.j=iCJXJminz二=5x1+x8=1f精品文檔x7+x8=1s.t.x3+x5W1x4+x5W1x5+x6+x7+x8W2xj=廠(chǎng)1選擇鉆探第sj井位10否4.5設(shè)xij為第i種泳姿用第名運(yùn)動(dòng)員.Si=1LJ=1aiJxiJminz二s.t.廠(chǎng)x11+x12+x13+x14+x15=1x21+x22+x23+x24+x25=1x31+x

26、32+x33+x34+x35=1x41+x42+x43+x44+x45=1x11+x21+x22+x23=1x12+x22+x32+x42=1x13+x23+x33+x43=1x14+x24+x34+x44=1jx15+x25+x35+x45=1xij=1或0(i=1,2,3,4j=1,2,3,4,5)由exce丨計(jì)算得出；張游仰泳，王游蛙泳，趙游自由泳，預(yù)期總成績(jī)?yōu)?26.2s.趙戔吐三胃戲和巾澈10000L=L圭法010D01=L闕00100=IJ由濁000L0L=Lkfo11LL0=111137.70000033.10000Q30.SOO00。猖：0圭計(jì)遠(yuǎn):乙as.138.92S.50i

27、QZm底劉精品文檔精品文檔自由泳總計(jì)mini33.328.538.930.433.629.226.429.62S.531.1趙錢(qián)張王周X11X12X13X14X15x21x22x23XZ4X25x31k32x33K14畑x41艾翌艾43x44x45超錢(qián)張王罔fl010000010010001000011110=111110033800c0034.70fl28.fi00029.2000028.533.834.70I屹氐2二規(guī)劃東豊戲到一躺可睛足所有的淅酬優(yōu)杭兄.WH.K.-鼎M很吉*JF-.、竄定|醉I|慍存方乘一用助26),E點(diǎn):d2-=4,d3-=0min2d2-+d3-二8,F點(diǎn):d2-=

28、0,d3-=4,min2d2-+d3-=4,故選F點(diǎn)程序法優(yōu)完級(jí)別約束燈釣束垃3020二侷差（1-負(fù)偏蓉d-約束關(guān)系nin.d.1-uind4+優(yōu)完級(jí)別約束燈釣束垃3020二侷差（1-負(fù)偏蓉d-約束關(guān)系nin.d.1-uind4+011000004004024305040243050_-_-果報(bào)報(bào)爲(wèi)性値說(shuō)一於杜尤先級(jí)別約束幻約束癥正偏差d+負(fù)脩差辻約束關(guān)系24301=040=400Q024二240030-30004080=50indl-0現(xiàn)劃求輝結(jié)具処劃浮朗懾乳一繫,T酒足所nr約更及品優(yōu)It?-很吉用越匱翹劃鑽鯉證電恆叭群a空存萬(wàn)案.幫WHQAEZZcDEF&HJ1憂(yōu)先轂別約束xl約束濾匸俏

29、差日+粧偏差4|約束2dl242610o404fl3420024244d30430305d400cO506攝劃求解找到一辭，可満足所有的豹束更最血狀竝o70規(guī)國(guó)驚聽(tīng)果89_衛(wèi)12i:i:i2d2：00:ind4-0-n護(hù)!,:I:衛(wèi)!.=孔-.“-13：i-：LGJ_L81920爾定6.4a破圈法避圈法3721873442最小部分樹(shù)166.4b最小部分樹(shù)32172頁(yè)6.114.22.63.71.71.70.81.11.4v0v1v2v3v40.90.822.4.22.63.71.71.70.81.11.4v0v1v2v3v40.90.822.81.82.9紅色曲線(xiàn)為使用一年賣(mài)出藍(lán)色曲線(xiàn)為使用兩

30、年賣(mài)出綠色曲線(xiàn)為使用三年賣(mài)出紫色曲線(xiàn)為使用四年賣(mài)出最短路程為3.7萬(wàn)元，路徑為v0-v1-v4或v0-v2-v4或v0-v1-v2-v4三種方案分別為：第一年年初買(mǎi)新車(chē)，年末賣(mài)掉再買(mǎi)新車(chē)，一直用到第四年年末賣(mài)掉；第一年出買(mǎi)新車(chē)，用兩年后于第二年末賣(mài)掉再買(mǎi)新車(chē)，用兩年于第四年末賣(mài)掉；第一年出買(mǎi)新車(chē)，年末賣(mài)掉后再買(mǎi)新車(chē)，第二年末賣(mài)掉再買(mǎi)新車(chē)，再用兩年于第四年年末賣(mài)掉。由圖可知，若摩托車(chē)最多使用三年，答案仍然不變6.14b根據(jù)題意,先給發(fā)點(diǎn)vs標(biāo)號(hào)，由弧(vs,v2)得對(duì)v2進(jìn)行標(biāo)號(hào)(vs,1);弧(v2,v1)對(duì)v1標(biāo)號(hào)(v2,1);弧(vs,v3)得對(duì)v3進(jìn)行標(biāo)號(hào)(vs,1);弧(v3,v4)對(duì)

31、v4標(biāo)號(hào)(v3,1);弧(v3,v4)對(duì)v4標(biāo)號(hào)(v3,1);弧(v4,v5)對(duì)v5標(biāo)號(hào)(v4,1);弧(v5,vt)對(duì)vt標(biāo)號(hào)(v5,1);反向追蹤找出增廣鏈最大流為14，最小割集為(v1,v3)(v2,v3)(v2,vt)(v1,vt)6.14cvt（vt（v4,l）最大流13，無(wú)最小割集193頁(yè)-7.2表7-9194頁(yè)7.3b假定最初事件在時(shí)刻零出現(xiàn)，則有tES(1,2)=tES(1,3)=ES(1,4)=0tEFtEFtEFtEStEFtEStEFtEStEFtEStEF(1,2)=ES(1,3)=4(1,4)=8(2,5)=2(2,5)=5(5,8)=8(5,8)=15(8,9)=1

32、5(8,9)=20(5,7)=5(5,7)=7(1,2)+t(1,2)=2tEStEFtEStEFtEStEFtEStEFtEStEFtEStEFtEStEFtEStEFt(4,7)=8(4,7)=11(4,6)=8(4,6)=10(3,6)=4(3,6)=12(6,7)=12(6,7)=13(7,9)=13(7,9)=15(7,9)=20ES(6,9)=12tEF(6,9)=19最短周期為20tttLF(6,9)=LF(8,9)=LFtLS(8,9)=15tLS(7,9)=16tLS(6,9)=13tLF(5,8)=15tLS(5,8)=8tLF(5,7)=16tLS(5,7)=14tLS(

33、4,7)=10tLF(4,7)=13tLS(6,7)=15tLF(6,7)=16tLS(4,6)=10tLF(4,6)=13tLS(3,6)=5tLF(3,6)=13tLS(1,3)=1tLF(1,3)=5tLS(1,4)=0tLF(1,4)=8tLF(2,5)=8tLS(2,5)=5tLF(1,2)=5tLS(1,2)=3(6,7)(6,9(7,9)1_212131319151316(8,9)5152015162020203011關(guān)鍵路線(xiàn)為(1,4),(4,5),(5,8),(8,9)課堂作業(yè)1.柴油機(jī)生產(chǎn)計(jì)劃設(shè)x1,x2,x3,x4分別為一二三四季度計(jì)劃minz=11.4x1+11.55x

34、2+11.3x3+11.45x4s.t.x1W25x2W35Jx3W30 x4W10jx1+x2+x3+x4=70LPOPTIMUMFOUNDATSTEP3NO.ITERATIONS=OBJECTIVEFUNCTIONVALUENO.ITERATIONS=1)796.2500VARIABLEVALUEREDUCEDCOSTX125.0000000.000000X25.0000000.000000X330.0000000.000000X410.0000000.0000002)0.0000000.1500003)30.0000000.0000004)0.0000000.2500005)0.0000000.1000006)0.000000-11.550000ROWSLACKORSURPLUSDUALPRICES3Flic-Edk&曲RAporcsWxvAaHelpaeHlib%二、3eiu.2|EJ畠m耶空種.LPOPTIMUMFOUKDATSTEPi圖即nt爪eeOBJECTIVEFUNCTIONVALLEmin11.4x1-11.55x2-11,3x3+11.45x41)796.2500SrI-.k1=35x2=35VARIABLEVALUEREDUCEDCOSTk3-30Ml25.QOOMKJ(L000000 x4=105.000000(LQO