管理運(yùn)籌學(xué)課后習(xí)題詳解內(nèi)蒙古工業(yè)大學(xué)國際商學(xué)院張劍二九年一月2第2章線性規(guī)劃的圖解法X2X15336A（12/7,15/7）00051X1X2071A（02，06）2（1）有唯一最優(yōu)解A點(diǎn)，對(duì)應(yīng)最優(yōu)目標(biāo)函數(shù)值Z36。（2）無可行解。045X1X25882023X1X2071（3）有無界解。3241（1）可行域?yàn)?，3，A，3圍成的區(qū)域。（2）等值線為圖中虛線所示。（3）如圖，最優(yōu)解為A點(diǎn)（12/7,15/7）,對(duì)應(yīng)最優(yōu)目標(biāo)函數(shù)值Z69/7。3（4）無可行解。012X1X221（5）無可行解。22X1X26804可行域4（6）最優(yōu)解A點(diǎn)（20/3，8/3），最優(yōu)函數(shù)值Z92/3。0812X1X261682可行域A（20/3，8/3）3（1）標(biāo)準(zhǔn)形式4（2）標(biāo)準(zhǔn)形式（3）標(biāo)準(zhǔn)形式4解（1）標(biāo)準(zhǔn)形式50X1X23225416求解0518259432121SXX5標(biāo)準(zhǔn)形式210426319463121SXX069X1X261024可行域A（36，24）6最優(yōu)解為A點(diǎn)13266,84523112變?yōu)樽兓?。斜率由）（如右圖XXC0624X1X2101628可行域A（3，7）1047模型（1）X1150，X2150；最有目標(biāo)函數(shù)值Z103000。6（2）第2、4車間有剩余。剩余分別為330、15，均為松弛變量。（3）四個(gè)車間對(duì)偶價(jià)格分別為50、0、200、0。如果四個(gè)車間加工能力都增加1各單位，總收益增加5002000250。（4）產(chǎn)品1的價(jià)格在0，500變化時(shí)，最優(yōu)解不變；產(chǎn)品2的價(jià)格在4000，變化時(shí)，最優(yōu)解不變。（5）根據(jù)（4）中結(jié)論，最優(yōu)產(chǎn)品組合不變。8模型（1）XA4000，XB10000，回報(bào)金額60000。（2）模型變?yōu)閄A18000，XB3000。即基金A投資額為180005090萬，基金B(yǎng)投資額為300010030萬。7第3章線性規(guī)劃問題的計(jì)算機(jī)求解89第4章線性規(guī)劃在工商管理中的應(yīng)用10111213141516第5章單純形法1可行解A、C、E、F；基本解A、B、F；基本可行解A、F。2（1）標(biāo)準(zhǔn)形式（2）有兩個(gè)變量的值取0。由于有三個(gè)基變量、兩個(gè)非基變量，非基變量最優(yōu)解中取0。（3）解2,064,2106214820114201600216008312412241SXA（4）將X1S2代入約束方程組中可得。1,0,321SXS02021064321121SXA將對(duì)應(yīng)的向量化作，即的排序是根據(jù)標(biāo)準(zhǔn)化后，321,SX321,SX對(duì)應(yīng)向量中單位向量的位置而定的，兩者為一一對(duì)應(yīng)的關(guān)系。（5）此解不是基本可行解。由于基本可行解要求基變量的值全部為非負(fù)。173（1）解（2）該線性規(guī)劃的標(biāo)準(zhǔn)型為（3）初始解的基為，初始解為，此時(shí),321S20,54,0目標(biāo)函數(shù)值為0。（4）第一次迭代，入基變量為X2，出基變量為S3。4（1）單純形法0,92473MA431121XZX1X2X3X4次數(shù)XBCB4100BX301310770X40420197/4Z000041000X3005/211/419/41X1411/201/49/4Z420101019,4,4321X18（2）圖解法0X1X2726745225可行域A（9/4，0）5（1）解0,48412235MAX653215313XXXZX1X2X3X4X5X6次數(shù)XBCB1285000BX403211002020/3X5011101011110X601241001484Z00000012850000X40013/4101/488X5002/311/12011/12721/21X11211/31/12001/12412Z124100104400148X28013/4101/4832/3X50005/122/311/125/342X112101/61/301/64/3Z128440000140080X2801011/59/51/105X350018/512/51/543X1121009/52/51/52Z12853/512/521/50003/512/521/5841984,52,321ZX（2）解0,5824MIN643213131XXXXFX1X2X3X4X5X6次數(shù)XBCB121000BX402211004X50122010840X6011100155Z0000001210000X405/21011/208X311/21101/2041X601/22001/211Z1/21111/203/21011/2044,32FX6解0,16245MA5431431132AXXMAXZX1X2X3X4X5X6次數(shù)XBCB51300MBA1M142101105/20X5012101016ZM4M2MM0M5M14M32MM0010MX211/411/21/401/45/2101X503/2021/211/22114Z1/411/21/401/419/405/21/40M1/45/22X151421011020X5006111166Z52010505019750M550400611116Z5105050011205M此問題有無界解。7（1）解0,8123MAX54321152XXMXZX1X2X3X4X5次數(shù)XBCB31200MBX30221001111/20X5M1101188ZMM0MM3M12M0M08MX212111/20011/21X5M201/2115/2Z122M126M/2MM92M06M/2M0665M/225,54321XX將本解代入所有約束中發(fā)現(xiàn)，不滿足約束2，所以本題無可行解。（2）解0,281034MIN87654321857421687654321XXXXMXXXFX1X2X3X4X5X6X7X8次數(shù)XBCB43000MMMBX6M21/21001001050X7M1101001088COMMENT微微微微1有錯(cuò)誤21X8M1000100122Z4M3M/2MMMMMM44M33M/2MMM00020MX6M01/210210263X7M0101101166143M/2MM3M4MM3M4033M/2MM43M004M412M8X5001/41/2011/201312X7M03/41/2101/210342X1411/41/2001/200520Z413M/42M/2M02M/2M0023M/42M/2M023M/20M203MX50002/31/312/31/312X23012/34/302/34/3043X14102/31/302/31/304Z432/316/302/38/300011/316/30M2/3M8/3M2828,4,8765421ZXX（4）解0,162844MA75431653121XXXZX1X2X3X4X5X6X7次數(shù)XBCB31200M00BX5M422110041X60240001020100X704820001164Z4M2M2MMM0024M12M12MM0004MX12121/20001/44X600010011/2121X70060110112Z2410001/24300M01/28,2,4,76531ZX22由于存在非基變量檢驗(yàn)數(shù)為0，所以本題有無窮多解。23第6章單純形法的靈敏度分析與對(duì)偶1（1）為非基變量，所以只要保證即可。1X011ZC。240241CC（2）為基變量，所以有2X6218,MAX0MIN022222CCAJJJJJJ（3）為非基變量，所以只要保證即可。2S0222SSSZC。808222SSSCC2解第五章習(xí)題5（2）最終表為X1X2X3X4X5X6次數(shù)XBCB121000BX405/21011/208X311/21101/2041X601/22001/211Z1/21101/203/21001/204（1）為非基變量，所以只要保證即可。1X11ZC。2211CC（2）為基變量，所以有3X24021,1,MINMAX0I03321333CCAJJJJJJ（3）為非基變量，所以只要保證即可。S0222SSSZC。102122SSSCC3（1）解250,0MINMAX11111BDXBDIIBIIB（2）解5050,310MINMAX22222BBDXDIIBIIB（3）解1500150,0MINMAX332333BBDXDIIBIIB254解X1X2X3X4X5X6次數(shù)XBCB121000BX405/21011/208X311/21101/2041X601/22001/211Z1/21101/203/21001/204（1）解4,80MIN0MAX11111BDXBDIIBIIB（2）解108,1MIN4,8MAX0I02222222BBBDXDXIIBIIB（3）解3333345,10MIN0MAXBDXBDIIBIIB5（1）解為基變量，所以有1X2663,1,MIN0MIN0AX111111CCACJJJJJJ當(dāng)時(shí)，在上述范圍內(nèi)。所以，最優(yōu)解不變。21C（2），。增加15個(gè)單位的原料不會(huì)5572B452B使原最優(yōu)解變化。原材料的對(duì)偶價(jià)格為1。即增加一個(gè)單位的原材料可使總收益增加1。原料價(jià)格為067元。所以，有利。（3），。155B6031B（4）解1251332251321321ZCZPB由于檢驗(yàn)數(shù)滿足非正要求，最優(yōu)解不變，所以不用修改生產(chǎn)計(jì)劃。（5）解03523144452313141ZCZPB此時(shí)生產(chǎn)計(jì)劃不需要調(diào)節(jié)，由于新產(chǎn)品的檢驗(yàn)數(shù)為0。6答均為唯一最優(yōu)解，根據(jù)計(jì)算機(jī)輸出結(jié)果顯示，如果松弛變量或剩余27變量為0且對(duì)應(yīng)的對(duì)偶價(jià)格也為0，或存在取值為0的決策變量并且其相差值也為0時(shí)，可知此線性規(guī)劃為無窮多組解。7（1）解0,1520MIN211YYTSF（2）解0,234610MAX1221YYTSZ8（1）解無約束321213321,0,050MINYYTSF（2）解無約束321321321,0,6MAXYYTSZ9解280,2843MAX65432121XXXTSZX1X2X3X4X5X6次數(shù)XBCB123000BX401111004X5011201080X600110012Z0000001230000X111111004X5002111041X600110012Z1111000321004X111001016X5000311202X200110012Z12210300510310,6,321FZ29第7章運(yùn)輸問題1（1）解最小元素法求初始調(diào)運(yùn)方案銷地甲乙丙丁12505030024004003350150500產(chǎn)地合計(jì)4002503502001200位勢法求檢驗(yàn)數(shù)銷地1234U15250050300024001420400163073501505003產(chǎn)地合計(jì)4002503502001200V26172325閉回路法調(diào)整方案銷地1234102505030024004003350150500產(chǎn)地合計(jì)4002503502001200求檢驗(yàn)數(shù)銷地1234U102502350300024006121440011319143501505003產(chǎn)地合計(jì)4002503502001200V21172325檢驗(yàn)數(shù)都大于0，得到最優(yōu)調(diào)運(yùn)方案。運(yùn)費(fèi)為19800元。（2）解初始調(diào)運(yùn)方案為30銷地12345合計(jì)1505020030024002006003350150500產(chǎn)地合計(jì)4002503502002001400求檢驗(yàn)數(shù)銷地12345U11250235020002400200212322產(chǎn)地391435015033V121723250調(diào)整調(diào)運(yùn)方案銷地1234515050502400200產(chǎn)地3350150150求新的檢驗(yàn)數(shù)銷地12345U11250202005002400200182322產(chǎn)地312173501501500V121720250調(diào)整調(diào)運(yùn)方案銷地123451100200240015050產(chǎn)地3350150求新的檢驗(yàn)數(shù)銷地12345U112100222002024001502023502產(chǎn)地3101535025150231V121722252檢驗(yàn)數(shù)都大于0，得到最優(yōu)調(diào)運(yùn)方案。運(yùn)費(fèi)為19650元。（3）解新的運(yùn)價(jià)表為銷地1234合計(jì)12117232530021015301940032321202250040000150產(chǎn)地合計(jì)5502503502001350最優(yōu)調(diào)運(yùn)方案（求解過程略）銷地1234515025000300240000040030035015050041000050150產(chǎn)地合計(jì)5502503502001350運(yùn)費(fèi)為19600元。2解運(yùn)價(jià)表11，22，3456合計(jì)104040505030404013002030307070905060350030606080804070504400407070404030704071005M0M000M0300合計(jì)1501501501003502002501501600求解可得11223456合計(jì)100500100001503002150150000200005003000015002500400400100000001005000100100000300合計(jì)150150150100350200250150150032此外，還有其他解如下11223456合計(jì)100500150001503002150150000150005003000015002500400400100000001005000100505000300合計(jì)150150150100350200250150150011223456合計(jì)100500001001503002150150000200005003000025001500400400100000001005000100100000300合計(jì)150150150100350200250150150011223456合計(jì)100500001501503002150150000150005003000030001000400400100000001005000100505000300合計(jì)1501501501003502002501501500運(yùn)費(fèi)為485元。3解運(yùn)價(jià)表如下1234合計(jì)1600660720031，660720780032M700760042，M770830023MM650023，MM71503合計(jì)555217最優(yōu)生產(chǎn)方案為331234合計(jì)1210031，300032040042，000223002023，00303合計(jì)5552174解運(yùn)價(jià)表為甲乙ABCD合計(jì)甲01001502001802401600乙80080210601701700A15080060110801100B200210700140501100C180601101300901100D24017090508501100合計(jì)1100110014001300160012007700最優(yōu)調(diào)運(yùn)方案甲乙ABCD合計(jì)甲11000300200001600乙011000060001700A0011000001100B0001100001100C000010001001100D0000011001100合計(jì)1100110014001300160012007700調(diào)整后可得甲乙ABCD合計(jì)甲0030020000500乙00006000600A0000000B0000000C00001001000D0000000合計(jì)003002005001001100總運(yùn)費(fèi)表甲乙ABCD合計(jì)甲0045000400000085000乙00003600003600034A0000000B0000000C0000090009000D0000000合計(jì)004500040000360009000130000總運(yùn)價(jià)為130000元。5解運(yùn)價(jià)表為12345合計(jì)A5449526401100B5773696101000合計(jì)5003005506501002100最優(yōu)調(diào)運(yùn)方案12345合計(jì)A250300550001100B250006501001000合計(jì)5003005506501002100最低總成本為110700元。6（1）最小元素法確定的初始調(diào)運(yùn)方案為123合計(jì)A87415B35925C00010合計(jì)20102050123合計(jì)A1515B1010525C1010合計(jì)20102050（2）表上作業(yè)法求最優(yōu)調(diào)運(yùn)方案調(diào)整運(yùn)輸方案并求檢驗(yàn)數(shù)123合計(jì)123UA87415A107150B35925B101055C00010C10262合計(jì)20102050V20435123U123UA41150A63150B151061B20541C5254C2554V464V244123合計(jì)123合計(jì)A001515A006060B205025B6025085C05510C0000合計(jì)20102050合計(jì)602560145最優(yōu)調(diào)運(yùn)方案的總成本145元。（3）由于所有檢驗(yàn)數(shù)大于0，所以存在唯一解。（4）解123合計(jì)123UA87415A107150B35925B101055C00020C20262合計(jì)30102060V204123U123UA41150A43150B151061B25361C15254C51054V464V444123合計(jì)123合計(jì)A001515A006060B250025B750075C510520C0000合計(jì)30102060合計(jì)75060135最優(yōu)調(diào)運(yùn)方案的總成本135元。36第8章整數(shù)規(guī)劃1（1）（2）254173ZX43921ZX4182X39Z264021ZX無可行解39Z64037412ZX40521XZ22314672ZX751423ZX3142X0（3）61073421ZX69038421ZX620351X97601342ZX6153842ZX381052ZX1162Z3738394041424344454647第9章目標(biāo)規(guī)劃484950515253第10章動(dòng)態(tài)規(guī)劃1整個(gè)過程劃分成4各階段，設(shè)初始狀態(tài)為KS（1）K4時(shí)階段4本階段各終點(diǎn)本階段初始狀態(tài)E到終點(diǎn)的最短距離本階段最優(yōu)終點(diǎn)D133ED244E（2）K3時(shí)階段3本階段各終點(diǎn)本階段初始狀態(tài)D1D2到終點(diǎn)的最短距離本階段最優(yōu)終點(diǎn)C13254595D1C237104488D2C33584488D1，D2（3）K2時(shí)階段2本階段各終點(diǎn)本階段初始狀態(tài)C1C2C3到終點(diǎn)的最短距離本階段最優(yōu)終點(diǎn)B156118311851311C1，C2B2538821084128C2B354981985139C1，C2（4）K1時(shí)本階段各終點(diǎn)本階段初始狀態(tài)B1B2B3到終點(diǎn)的最短距離本階段最優(yōu)終點(diǎn)A113148513941313B1，B2則有最短路線長度為13。分別是（A，B1，C1，D1，E）；（A，B2，C2，D2，E）；（A，B1，C2，D2，E）。2按項(xiàng)目將整個(gè)過程劃分為3個(gè)階段分配給第K個(gè)項(xiàng)目到最后一個(gè)項(xiàng)目的資金。4KS1S分配給第K個(gè)項(xiàng)目的資金。X；KKXS1,MAX1KKKKSFSRSF54（1）K3時(shí),3XSR3XS012343SF3X046460170701276762388883488884（2）K2時(shí),32SFXSRX2S012342SF2X0464995950170491194652981190276491257052122466110712503884913776521287061131467111813704884913788521407661137707114146781241413（3）K1時(shí),21SFXSR1XS012341SF1X41414718813751188125591841197119095761711903則有分配方案為（3，0，1）。3按月將整個(gè)過程劃分為4個(gè)階段為第K個(gè)月月初庫存量。為第K個(gè)月的產(chǎn)量。KSKX；KKDXS1,MIN1KKKKSFXSRSF4,IINKKD（1）K4時(shí)55,4XSR4XS012344SFX0686831552232321306060（2）K3時(shí),43SFXSR3XS012343SF3X01158158421414214331221241261222（3）K2時(shí),32SFXSR2XS012342SF2X0224232243120821620820822191941981913164176181640（4）K1時(shí),21SFXSR1XS012341SF1X02522562582522521,4最有生產(chǎn)策略（1，3，4，3）；（4，0，4，3）。最低成本252。4按產(chǎn)品劃分階段，則共有4各階段。為裝載第K鐘產(chǎn)品前，還可以裝載的重量。為第K種產(chǎn)品的KSKX56裝載數(shù)量。；KKKDXS1,MAX1KKKKSFSRSF；KKKQR,KDX（1）K3時(shí),3XSR3XS0123SF3X0102031800418018015180180161801801718036018180360360291803603602101803603602（2）K2時(shí),32SFXSR2XS01232SF2X000012301401401418014018005180140180061801402802802718032028032018360320280360093603202804204203103603204604204602（2）K1時(shí)57,21SFXSR1XS0123451SF1X104604604804804005005005最優(yōu)策略（5，0，0）。5按年劃分成5各階段。為年初完好的機(jī)器數(shù)量。為第K年處于高負(fù)荷狀態(tài)下工作的KSKX機(jī)器數(shù)量。狀態(tài)轉(zhuǎn)移方程8051KKKXSXS階段指標(biāo)函數(shù)6,R最有指標(biāo)函數(shù)0,MAX610SFSFXSRSFKKKSKK（1）K5時(shí)，5X550101AXSSSFKS（2）K4時(shí)4440445440415MAX8061ASXSXXFSSFKKKSSSX（3）K3時(shí)333034330318518MAX064ASXSXSFXSXSFKKKSX5822202322024014MAX8586ASXSXFXSXSFKKKSSSX（5）K1時(shí)11101211013232MAX8054064ASXSXFXSXSFKKKSSSX由于125，代入。1S7905萬元F6按工廠劃分成4個(gè)階段。第K期初剩余金額。為第K期投入的金額。KSKX狀態(tài)轉(zhuǎn)移方程KS1階段指標(biāo)函數(shù)DR（1）K4時(shí),4XSR4XS01234564SF4X0000128281247472365653474744580805（2）K3時(shí),43SFXSR3XS01234563SFX000010282818018281592047471828463903947030656518476539286761061672407474186583394786612889780788935080801874923965104614710878281069009010836085851880983974113616512678471259028118950951263（3）K2時(shí),32SFXSR2X2S01234562SFX000010282825025280204747252853450455313067672547724528735705773240898925679245479257288565065921，2501081082589114456711257471146528947007011416012612625108133458913457671246547112702898730731342（4）K1時(shí),21SFXSR1XS01234561SFX60134134201141344292134607313375531288528113900901340,1,2則有，最優(yōu)策略為（0，2，3，1）；（1，1，3，1）；（2，1，2，1）；（2，2，0，2），對(duì)應(yīng)最優(yōu)解134。7按照地區(qū)劃分為3各階段。第K期初可供分配的商店數(shù)。為第K期投建的商店數(shù)。KSKX狀態(tài)轉(zhuǎn)移方程KKS1階段指標(biāo)函數(shù)DR（1）K3時(shí)，地區(qū)1,3XSR3X0123453SFX603S000013312772312123414144515155（2）K2時(shí)，地區(qū)2,32SFXSR2XS0123452SFX00001033505512077538100101023012125712103131401414340141451217107171431716016171，2，350151551419101222147211631916016222（3）K1時(shí)，地區(qū)3,21SFXSR1XS0123451SFX5022224172171421910191051511011220則最優(yōu)策略為（3，2，0）。8按年劃分成5個(gè)階段。為機(jī)器使用的年數(shù)。當(dāng)年為更新費(fèi)用，為使用年的機(jī)器維護(hù)TCOT費(fèi)用。期初機(jī)器已使用的年數(shù)。本年機(jī)器是否更新。KSKXKRF,MIN10TGTORCTRIJIJI（1）K5時(shí)615R5XSRK5FX1513186066K2513188088K3513181101111K4513181801818K,R5513181801818R（2）K4時(shí)4R4XSRK4FX1512623681414K25126238111919K351262311182923R451262318213923R（3）K3時(shí)3R3XSRK3FX151214316192525K251214318233131K，R3512143111233431R（4）K2時(shí)2R2XSRK2FX151125416313737K251125418313939K（5）K1時(shí)1R1XSRK1FX151137536394545K62最優(yōu)策略為（K，K，R，K，K）。9以周為單位劃分成6個(gè)階段。（1）K6時(shí)，66SF50F506F606F（2）K5時(shí)74325E60,57,5SSF當(dāng)當(dāng)當(dāng)（3）K4時(shí)5430254E60,54,444SSF當(dāng)當(dāng)當(dāng)（4）K3時(shí)45330253E60,453,33SSF當(dāng)當(dāng)當(dāng)（5）K2時(shí)85240252E60,852,222SSF當(dāng)當(dāng)當(dāng)（6）K1時(shí)15743051E6360,1575,1SSF當(dāng)當(dāng)當(dāng)最優(yōu)策略為在前4周如市價(jià)為500元時(shí)，立即購買。否則等待。在第五周市價(jià)為500或550時(shí)購買，否則等待。10按月劃分為3個(gè)階段。為期初有合格品；為期初無合格品。本期試制數(shù)量。0KS1KSKXKKXKXKSP321010,52KKXOC（1）K3時(shí)321523X3XS01234563SFX011513511179949469489819464（2）K2時(shí)2346952XX2XS01234562SFX001946988783837875933833（3）K1時(shí)1328521X1XS0123451SFX1839038197968148597963第一月、第二月試制3個(gè)，第三月試制4個(gè)。6411按月劃分成4個(gè)階段。期初庫存。本期訂貨量。KSKX（1）K4時(shí)444101,SXSXF（2）K3時(shí)，34S33343090,SXSXSXF（3）K2時(shí)，2S22324708,SXSXF（4）K1時(shí)，12S13504045,21SXX