線性規(guī)劃單純形法

1、吉林建筑工程學(xué)院城建學(xué)院人文素質(zhì)課線性規(guī)劃單純形法例題【8頁(yè)1.4(1)】分別用圖解法和單純形法求解線性規(guī)劃問(wèn)題。max z 2x1 x23x1 5x215(s.t) 6x! 2x224xx20在上述線性規(guī)劃問(wèn)題中，分別加入松馳變量x3,x4,得到該線性規(guī)劃問(wèn)題的 標(biāo)準(zhǔn)型max z2為X20x30x43x15x2X315(s.t)6x12x2x424X1,X2, X3,X40選擇x3, x4為初始基變量,Cj2100iCBXbbX1X2X3X40X315351015E 5;0X42462012 46Cj Zj210015 24min ,436,2(0 3 0 6)21 (0 50 2)3 0(

2、0100)04 0(0001)0所以選擇為為進(jìn)基變量，x4為出基變量Cj2100iCBXbbXiX2X3X40X33041-1/2342Xi411/301/6121/3Cj Zj01/30-1/33 4min , 3/44 1/31 2(0021) 02 1(0421/3)1/330(0120) 04 0(01/22 1/6)1/3所以選擇X2為進(jìn)基變量，X3為出基變量Cj2100iCBXbbX1X2X3X41X23/4011/4-1/82X115/410-1/125/24Cj Zj00-1/12-7/2412(10 21)021(11 20)030(11/421/12)1/124 0(11/

3、825/24)7/24所以，最優(yōu)解為x (x2, x1)T (15,3)T,4 415333故有：max z 2x1 x22 -444【8頁(yè)1.4(2)】分別用圖解法和單純形法求解線性規(guī)劃問(wèn)題。max z 2xi 5x2x,122x212(st)3x1 2x218x1, x20在上述線性規(guī)劃問(wèn)題中，分別加入松馳變量x3,x4,x5,得到該線性規(guī)劃問(wèn)題的 標(biāo)準(zhǔn)型max z2x-iX20x3 0x40x5X1X34(st)2x2X4243x12x2X518X1,X2,X3, X4, X50Cj25000iCBXbbX1X2X3X4X50X34101014 00X4120201012620X5183

4、200018c92Cj Zj2500012 18廠min ,一,62 21 2(010003)22 5( 000202)53 0(010000)04 0(000100)05 0(010000)0所以選擇X2為進(jìn)基變量，X4為出基變量Cj25000iCBXbbX1X2X3X4X50X34101004 -415X260101/20600X56300-11623Cj Zj200-5/20.46_min , ，2131 2(015003)22 5(005100)03 0(015000)04 0 (0 0 5 1/2 01)5/25 0 (0 1 5 0 0 1) 0所以Xj為進(jìn)基變量，x5為出基變量Cj25000iCbXbbX1X2X3X4X50X320011/3-1/35X260101/202X12100-1/31/3Cj Zj000-11/6-2/312(005021)025(005120)030(015020)040(01/351/2