大連大學(xué)2010/2011學(xué)年第一學(xué)期期中考試卷90分鐘（共4)姓名學(xué)號(hào)一二121234學(xué)院一、用圖解法求解（10分）給定下述線性規(guī)劃問(wèn)題：maxzx2x密1212x3x1212封閉卷z3線23zcxi1j1xxxxa1xxxxab12xxxxb2xxb3xxb4x0maxwauaubvbvbvbv112211223344uvc11uvc12uvc13uv014uvc21uvc22uvc23uv024,,,,,無(wú)符號(hào)限制uuvvvv121234三、計(jì)算題（每小題20分，共80分）1.用單純形法求解下列線性規(guī)劃問(wèn)題(列出計(jì)算過(guò)程)。minz3x5x12x812x1223x4x3612x,x012MaxW3x5000xxxx12345x8x13標(biāo)準(zhǔn)化：2x12x42xx3x436125,,,,0xxxxx12345變量變量，第二步標(biāo)準(zhǔn)化)列單純形表計(jì)算：CB基-3-5000b100081000101236-3-3-5czjj最優(yōu)解X=（3，5，0，0,0），最優(yōu)值W=34,故Z=-34**T2.用單純形法中兩階段法求解下述線性規(guī)劃問(wèn)題(列出計(jì)算過(guò)程)。(注意步驟，區(qū)分人工變量與松馳變量)minz4xx123xx3124x3xx6123x2xx4124x0,i1,2,3,4imaxz4xx'123xx3(1)(2)124x3xx6123x2xx41240,i1,2,3,4ximinwxx563xxx31254x3xxx61236x2xx4124x0,i1,2,3,4,5,6ib001000010001364j1/3[5/3]1/3-4/312X-10-160010001000103j3/5-1/53/5-4/53/56/5-1-1100-1czjjmaxz4xx0x0x1234b10001000010001003/56/51j-1/52/59/510-1/5czjj29175(,,1,0,0,0),ZX553.用對(duì)偶單純形法求解下述線性規(guī)劃問(wèn)題(列出計(jì)算過(guò)程)。(此問(wèn)題不是加人工變量，而是根據(jù)對(duì)偶理論，在保持對(duì)偶問(wèn)題為可行解的基礎(chǔ)上，通過(guò)迭代，使原問(wèn)題也達(dá)到可行解，即得到了目標(biāo)函數(shù)的最優(yōu)解。)minz4x12x18x123x3x3132x2x523x,x,x0123解：先將問(wèn)題改寫(xiě)為：maxw4x12x18x0x0x12345x3xx31342x2xx5235x0,i1,2,3,4,5imaxw4x12x18x0x0x12345x3xx31342x2xx5235x0,i1,2,3,4,5ic00j基CbxxxB2450011001000100x40czjjjj0x41x2cz01j10010x2cz00jX=(03/2100),minz=364.已知某運(yùn)輸問(wèn)題的產(chǎn)銷(xiāo)數(shù)量表與單位運(yùn)價(jià)表如表4-1，用表上作業(yè)法求最優(yōu)解(列出計(jì)算過(guò)程)。表4-1A產(chǎn)量93481047256銷(xiāo)量34A產(chǎn)量333844銷(xiāo)量62（3）02214B1B2B3B4產(chǎn)量3844銷(xiāo)量36B1B2B3B4產(chǎn)量3844銷(xiāo)量36（4）（-1）（2）226（3）-4618產(chǎn)地銷(xiāo)地B1B2B3B4產(chǎn)量銷(xiāo)量3846位勢(shì)法檢驗(yàn)：（1）（4）71（4）3（3）2-4（10）42（2）