線性規(guī)劃單純形法

《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1.4(1)】分別用圖解法和單純形法求解線性規(guī)劃問題。maxz=2x+x3x+5x<15(s.t)]6x+2x<24、x,x>0在上述線性規(guī)劃問題中，分別加入松馳變量x3,x4，得到該線性規(guī)劃問題的標(biāo)準(zhǔn)型maxz=2x+x+0x+0x3x+5x+x=15(st)6x+2x+x=24x,x,x,x>0V12 3 4選擇％,氣為初始基變量，cj21000.cXbbxxxx0x153510字5；0x24[6]20124=4c-z,2100-?[15241』min[亍商=4b=2-(0x3+0x6)=2b=1-(0x5+0x2)=12b=0-(0x1+0x0)=03b=0-(0x0+0x1)=04所以選擇氣為進(jìn)基變量，x4為出基變量。c21000.

cxbbxxxx0x30[4]1-1/232x411/301/6—=121/3c-z01/30-1/3mln{4,1/3卜3/4b=2-(0x0+2x1)=0b=1-(0x4+2x1/3)=1/32b=0-(0x1+2x0)=03b=0-(0x-1/2+2x1/6)=-1/34所以選擇％為進(jìn)基變量，％為出基變量。cj21009cxbbxxxx1x3/4011/4-1/82x15/410-1/125/24c-z00-1/12-7/24b=2-(1x0+2x1)=0b=1-(1x1+2x0)=02b=0-(1x1/4+2x-1/12)=-1/123b=0-(1x-1/8+2x5/24)=-7/244153所以，最優(yōu)解為X=(%,氣)T=(---,-)T,15.333故有：maxz=2x+x=2x—+—=—【8頁1.4(2)】分別用圖解法和單純形法求解線性規(guī)劃問題。maxz=2x+5xIXi<12(s.t)<x<12(s.t)<2氣+2x2<18、氣，x2>0在上述線性規(guī)劃問題中，分別加入松馳變量尤,x,x，得到該線性規(guī)劃問題的標(biāo)準(zhǔn)型3 4 5maxz=2x+x+0x+0x+0xx+x=4(s.t)< 2x2+x4 =243氣+2x2+ x5=18x,x,x,x,x>0、 1 2 3 4 5cj250009cXbbxxxxx0x4101014_0x120[2]01012=60x1832000與=9c-z25000-?I12181右minfa卜6b=2-(0x1+0x0+0x3)=2b=5-(0x0+0x2+0x2)=5b=0-(0x1+0x0+0x0)=03b=0-(0x0+0x1+0x0)=04b=0-(0x1+0x0+0x0)=05所以選擇x2為進(jìn)基變量，x4為出基變量。

cj250000.cXBbxxxxx0x4101004=45x60101/206=_0x6[3]00-11j=2c-z,200-5/20min｛『,3卜2b=2-(0x1+5x0+0x3)=2b=5-(0x0+5x1+0x0)=0b=0-(0x1+5x0+0x0)=03b=0-(0x0+5x1/2+0x-1)=-5/24b=0-(0x1+5x0+0x1)=05所以氣為進(jìn)基變量，七為出基變量cj250000.cXbbxxxxx0x20011/3-1/35x60101/202x2100-1/31/3c-z,000-11/6-2/3b=2-(0x0+5x0+2x1)=0b=5-(0x0+5x1+2x0)=0b=0-(0x1+5x0+2x0)=03b=0-(0x1/3+5x1/2+2x-1/3)=-11/64b=0-(0x-1/3+5x