例minz=10x1+9x2 s.t.6x1+5x2≤60 10x1+20X,≥150 X1≤8 0 引入松弛变量x3,x4,x3,将不等式化为等式,即单纯形标准形 min z=10x,+9x s.t.6X1+5X2+x3=60 10X1+20X =150 XI+xs= 8 X≥0(i=1,2,3,4,5) 系数矩阵为 65100 A=|10200-10=(P1P2P3P4P) 000 b=(60,150,8) 显然A的秩ran(A)=3,任取3个线性无关的列向量如P3P4P称为 组基,记为B.其余列向量称为非基,记为N例 min z = 10x1 + 9x2 s．t．6x1 + 5x2 ≤ 60 10x1 + 20x2 ≥ 150 x1 ≤ 8 x1 , x2 ≥ 0 引入松弛变量x3 , x4 , x5 , 将不等式化为等式, 即单纯形标准形: min z = 10x1 + 9x2 s．t．6x1 + 5x2 + x3 = 60 10x1 + 20x2 - x4 = 150 x1 + x5 = 8 xi≥ 0 (i = 1,2,3,4,5) 系数矩阵为: 6 5 1 0 0 A = 10 20 0 -1 0 = (P1 P2 P3 P4 P5 ) 1 0 0 0 1 b = (60, 150, 8 ) T 显然A的秩ran(A)=3, 任取3个线性无关的列向量,如P3 P4 P5称为 一组基, 记为B. 其余列向量称为非基, 记为N