第一章

P43-1.1（1）

当取A（6/5,1/5）或B（3/2,0）时，z取最小值3。所以该问题有无穷多最优解，所有线段AB上的点都是最优解。

P43-1.2(1)

''''令x4?x4?x4，z??z

maxz?3x1?4x2?2x3?5x4?5x4

''''?4x1?x2?2x3?x4?x4?2x1?x2?x3?2x4?2x4?x5?14?2x1?3x2?x3?x?x?x6?2x1,x2,x3,x4,x4,x5,x6?0''''4''4''''''

P43-1.4(1) 图解法：

A(0,9/4)，Z1=45/4；B(1,3/2)，Z2=35/2；C(8/5,0)，Z3=16。

单纯形法：

Cb 0 0 Xb x3 x4 δ b 9 8 10 x1 3 5 10 5 x2 4 2 5 14/5 2/5 1 1 0 0 0 x3 1 0 0 1 0 0 5/14 -1/7 -5/14 0 x4 0 1 0 -3/5 1/5 -2 -3/14 2/7 -25/14 θ 3 8/5 3/2 4 0 10 x3 x1 δ 21/5 8/5 0 1 0 0 10 x2 x1 δ 3/2 1 0 1 0 依次相当于：原点；C；B。

P44-1.7(1) 大M法：

Cb Xb b 2 x1 -1 x2 2 x3 0 x4 0 x5 0 x6 -M x7 -M x8 -M x9 θ -M -M -M -M -M -1 -M 2 -1 2 2 -1 无界解。 x7 x8 x9 δ x7 x8 x2 δ x7 x3 x2 δ x1 x3 x2 δ 6 2 0 6 2 0 3 2 1 3/4 7/2 7/4 1 1 1 -2 0 1 0 2 -1 -M+2 3 M-1 M+2 1 0 3/2 -2 0 1 0 1 -1/2 -M+ 0 2.5M+ 4 0 0 -2 0 1 -1 1 0 4M+5 0 0 1 0 0 0 0 1 0 1 0 0 0 0 -1 0 0 1 0 0 0 -1 0 0 1 0 0 0 -1 0 0 1 -M -M -M 0 0 0 -1 0 1/2 1 0 -1/2 0 -1 0 0 1 0 0 0 -1/2 0 0 1/2 -M -M 0.5M- 0 0 -1.5M+ -1 3/2 1/2 1 -3/2 -1/2 0 -1 0 0 1 0 0 -1/2 -1/2 0 1/2 1/2 -M 1.5M+ 0.5M- 0 -2.5M- -1.5M+ -1/4 3/8 1/8 1/4 -3/8 -1/8 -1/2 -1/4 1/4 1/2 1/4 -1/4 -1/4 -1/8 -3/8 1/4 1/8 3/8 5/4 -3/8 -9/8 -M- -M+ -M+ 6 - 0 4 2 两阶段法： 阶段一：

Cb -1 -1 -1 -1 -1 0 -1 0 0 0 0 0 Xb b x7 6 x8 2 x9 0 δ x7 6 x8 2 x2 0 δ x7 3 x3 2 x2 1 δ x1 3/4 x3 7/2 x2 7/4 δ 0 x1 1 -2 0 -1 1 -2 0 -1 4 -2 -1 4 1 0 0 0 2 x1 1 0 0 0 x2 1 0 2 3 0 0 1 0 0 0 1 0 0 0 1 0 -1 x2 0 0 1 0 x3 1 1 -1 1 3/2 1 -1/2 5/2 0 1 0 0 0 1 0 0 2 x3 0 1 0 0 x4 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1/4 -1/2 -1/4 0 0 x5 0 -1 0 -1 0 -1 0 -1 3/2 -1 -1/2 3/2 3/8 -1/4 -1/8 0 0 x4 -1/4 -1/2 -1/4 0 x6 0 0 -1 -1 1/2 0 -1/2 1/2 1/2 0 -1/2 1/2 1/8 1/4 -3/8 0 0 x5 3/8 -1/4 -1/8 -1 x7 1 0 0 0 1 0 0 0 1 0 0 0 1/4 1/2 1/4 -1 0 x6 1/8 1/4 -3/8 -1 x8 0 1 0 0 0 1 0 0 -3/2 1 1/2 -5/2 -3/8 1/4 1/8 -1 θ -1 x9 0 0 1 0 -1/2 0 1/2 -3/2 -1/2 0 1/2 -3/2 -1/8 -1/4 3/8 -1 θ 6 - 0 4 2 阶段二： Cb Xb b 2 x1 3/4 2 x3 7/2 -1 x2 7/4 δ 无界解。

0 0 0 5/4 -3/8 -9/8 P45-1.10

证明：CX(0)>=CX*，C*X*>=C*X(0)? CX(0)-CX*+C*X*-C*X(0)>=0，即(C*-C)(X*-X(0))>=0。

P45-1.13

设饲料i使用xi （kg），则

minz?0.2x1?0.7x2?0.4x3?0.3x4?0.8x5

s.t. 3x1?2x2?x3?6x4?18x5?700 x1?0.5x2?0.2x3?2x4?0.5x5?30

0.5x1?x2?0.2x3?2x4?0.8x5?100

x1,x2,x3,x4,x5?0

第二章

P74-2.1(1)

maxw?2y1?3y2?5y3

y1?2y2?y3?2 3y1?y2?4y3?2 4y1?3y2?3y3?4 y1?0,y2?0,y3无约束

P75-2.4

maxw?2y1?3y2y1?2y2?22y1?y2?33y1?y2?5y1?3y2?6y1?0,y2?0(1)

(2) (8/5,1/5)

(3) 无穷多最优解。x2?85?x1,x3?x1?75,x4?0