运筹学资料1线性规划课件.ppt

1、产产品品（万万件件）原原料料（公公斤斤）A B C D 提提供供量量 甲 3 2 10 4 18 乙 0 0 2 1/2 3 利利润润（万万元元/万万件件）9 8 50 19 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 10 4 1 0 18 0 x6 0 0(2)1/2 0 1 3 9 8 50 19 0 0 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 10 4 1 0 18 0 x6 0 0 1 1/4 0 1/2 3/2 cj 9 8 50 19 0 0 cB XB x

2、1 x2 x3 x4 x5 x6 b 0 x5 3 2 10 4 1 0 18 0 x6 0 0(2)1/2 0 1 3 9 8 50 19 0 0 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 0 3/2 1-5 3 50 X3 0 0 1 1/4 0 1/2 3/2 9 8 0 13/2 0-25 75 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 10 4 1 0 18 0 x6 0 0 1 1/4 0 1/2 3/2 cj 9 8 50 19 0 0 cB XB x1 x

3、2 x3 x4 x5 x6 b 0 x5 3 2 0 3/2 1-5 3 50 X3 0 0 1 1/4 0 1/2 3/2 9 8 0 13/2 0-25 75 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 0 3/2 1-5 3 50 X3 0 0 1 1/4 0 1/2 3/2 9 8 0 13/2 0-25 75 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 9 X1 1 2/3 0 1/2 1/3-5/3 1 50 X3 0 0 1 1/4 0 1/2 3/2 cj 9 8 50 19

4、0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 0 3/2 1-5 3 50 X3 0 0 1 1/4 0 1/2 3/2 9 8 0 13/2 0-25 75 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 9 X1 1 2/3 0 1/2 1/3-5/3 1 50 X3 0 0 1 1/4 0 1/2 3/2 0 2 0 2-3-10 84 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 0 3/2 1-5 3 50 X3 0 0 1 1/4 0 1/2 3/2 9

5、8 0 13/2 0-25 75 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 8 X2 3/2 1 0 3/4 1/2-5/2 3/2 50 X3 0 0 1 1/4 0 1/2 3/2 -3 0 0 1/2-4-5 37 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 9 X1 1 2/3 0 1/2 1/3-5/3 1 50 X3 0 0 1 1/4 0 1/2 3/2 0 2 0 2-3-10 84 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 8 X2 2 4/3 0

6、 1 2/3-10/3 2 50 X3 0 0 1 1/4 0 1/2 3/2 -3 0 0 1/2-4-5 37 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 8 X2 3/2 1 0 3/4 1/2-5/2 3/2 50 X3 0 0 1 1/4 0 1/2 3/2 -3 0 0 1/2-4-5 37 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 cj 9 8 50 19 0 0 cB XB x1 x2

7、 x3 x4 x5 x6 b 8 X2 2 4/3 0 1 2/3-10/3 2 50 X3 0 0 1 1/4 0 1/2 3/2 -3 0 0 1/2-4-5 37 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3 2 10 4 1 0 18 0 x6 0 0 2 1/2 0 1 3 9 8 50 1

8、9 0 0 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 0 x5 3

9、2 10 4 1 0 18 0 x6 0 0 2 1/2 0 1 3 9 8 50 19 0 0 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9+a

10、8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0

11、1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 1 2/3 0 1/2 1/3-5/3 1 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2

12、/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 9+a X1 1 2/3 0 1/2 1/3-5/3 1 50 X3 0 0 1 1/4 0 1/2 3/2 0 6-2a 3 0 4-a 2-9-a 3 5a-30 3 84+a cj 9+a 8 50 19 0 0

13、 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 1 2/3 0 1/2 1/3-5/3 1 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4+a-2/3 0 0-13/3-10/3 88 cj 9+a 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 9+a X1 1 2/3 0 1/2 1/3-5/3 1 50 X3 0 0 1 1/4 0 1/2 3/2 0 6-2a 3 0 4-a 2-9-a 3 5a-30 3 84+a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3

14、0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50+a 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50+a X3-1/2-1/3 1 0-1/6 4/3 1 a-8 2 a-23 0 0 a-266-4a-10 3 88+a cj 9 8 50+a 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50+a X3-1/2-1/3 1 0-1/6 4

15、/3 1 a-8 2 a-23 0 0 a-266-4a-10 3 88+a cj 9 8 50+a 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50+a X3-1/2-1/3 1 0-1/6 4/3 1 a-8 2 a-23 0 0 a-266-4a-10 3 88+a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj

16、9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2+(2/3)a 50 X3-1/2-1/3 1 0-1/6 4/3 1-(1/6)a -4-2/3 0 0-13/3-10/3 88+(13/3)a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2+(2/3)a 50 X3 3/2 1-3 0 1/2-4 (1/2)a-3 -4-2/3 0 0-13/3-10/3 88+(13/3)a cj 9 8 50 19 0 0 cB

17、 XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2+(2/3)a 50 X3-1/2-1/3 1 0-1/6 4/3 1-(1/6)a -4-2/3 0 0-13/3-10/3 88+(13/3)a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2+(2/3)a 50 X3 3/2 1-3 0 1/2-4 (1/2)a-3 -4-2/3 0 0-13/3-10/3 88+(13/3)a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4

18、x5 x6 b 19 X4 0 0 4 1 0 2 6 8 X2 3/2 1-3 0 1/2-4 (1/2)a-3 -3 0-2 0-4-6 90+4a cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 0 0 4 1 0 2 6 8 X2 3/2 1-3 0 1/2-4 (1/2)a-3 -3 0-2 0-4-6 90+4a cj 9 8 50 19 0 0 17 cB XB x1 x2 x3 x4 x5 x6 x 7 b 19 X4 2 4/3 0 1 2/3-10/3-4/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 5/6

19、1 -4-2/3 0 0-13/3-10/3 2/3 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 17 cB XB x1 x2 x3 x4 x5 x6 x 7 b 19 X4 2 4/3 0 1 2/3-10/3-4/3 2 50 X3-3/5-2/5 6/5 0-1/5 8/5 1 6/5 cj 9 8 50 19 0 0 17 cB XB x1 x2 x

20、3 x4 x5 x6 x 7 b 19 X4 2 4/3 0 1 2/3-10/3-4/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 5/6 1 -4-2/3 0 0-13/3-10/3 2/3 88 cj 9 8 50 19 0 0 17 cB XB x1 x2 x3 x4 x5 x6 x 7 b 19 X4 6/5 4/5 8/5 1 2/5-6/5 0 18/5 17 X7-3/5-2/5 6/5 0-1/5 8/5 1 6/5 -18/5-2/5-4/5 0-21/5-22/5 0 88(4/5)cj 9 8 50 19 0 0 17 cB XB x1 x2 x3 x4

21、x5 x6 x 7 b 19 X4 2 4/3 0 1 2/3-10/3-4/3 2 50 X3-3/5-2/5 6/5 0-1/5 8/5 1 6/5 cj 9 8 50 19 0 0 17 cB XB x1 x2 x3 x4 x5 x6 x 7 b 19 X4 6/5 4/5 8/5 1 2/5-6/5 0 18/5 17 X7-3/5-2/5 6/5 0-1/5 8/5 1 6/5 -18/5-2/5-4/5 0-21/5-22/5 0 88(4/5)cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-1

22、0/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 4 3 5 2 0 0 1 8 -4-2/3 0 0-13/3-10/3 0 88 cj 9 8 50 19 0 0 cB XB x1 x2 x3 x4 x5 x6 b 19 X4 2 4/3 0 1 2/3-10/3 2 50 X3-1/2-1/3 1 0-1/6 4/3 1 -4-2/3 0 0-13/3-10/3 88 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1

23、0-1/6 4/3 0 1 0 X7 4 3 5 2 0 0 1 8 -4-2/3 0 0-13/3-10/3 0 88 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 0 1/3 5 0-4/3 20/3 1 4 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0

24、 1 0 X7 4 3 5 2 0 0 1 8 -4-2/3 0 0-13/3-10/3 0 88 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 5/2 2 0 0-1/2 0 1-1 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 0 1/3

25、5 0-4/3 20/3 1 4 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 5/2 2 0 0-1/2 0 1-1 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7-5 -4 0 0 1 0-2 2 cj 9 8 50 19 0 0 0 cB

26、XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7 5/2 2 0 0-1/2 0 1-1 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 16/3 4 0 1 0-10/3 4/3 2/3 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7-5 -4 0 0 1 0-2 2 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 2 4/

27、3 0 1 2/3-10/3 0 2 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7-5 -4 0 0 1 0-2 2 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 16/3 4 0 1 0-10/3 4/3 2/3 50 X3-4/3-1 1 0 0 4/3-1/3 4/3 0 X5-5 -4 0 0 1 0-2 2 -77/3-18 0 0 0-10/3-26/3 79.5 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 16/3 4 0 1 0-

28、10/3 4/3 2/3 50 X3-1/2-1/3 1 0-1/6 4/3 0 1 0 X7-5 -4 0 0 1 0-2 2 cj 9 8 50 19 0 0 0 cB XB x1 x2 x3 x4 x5 x6 X7 b 19 X4 16/3 4 0 1 0-10/3 4/3 2/3 50 X3-4/3-1 1 0 0 4/3-1/3 4/3 0 X5-5 -4 0 0 1 0-2 2 -77/3-18 0 0 0-10/3-26/3 79.5 影子价格是对系统资源的最优估影子价格是对系统资源的最优估影子价格是对系统资源的最优估影子价格是对系统资源的最优估影子价格是对系统资源的最优估影子价

29、格是对系统资源的最优估计，只有系统达到最优状态时才可计，只有系统达到最优状态时才可计，只有系统达到最优状态时才可计，只有系统达到最优状态时才可计，只有系统达到最优状态时才可计，只有系统达到最优状态时才可能赋与资源这种价值。因此，也称能赋与资源这种价值。因此，也称能赋与资源这种价值。因此，也称能赋与资源这种价值。因此，也称能赋与资源这种价值。因此，也称能赋与资源这种价值。因此，也称为最优价格。为最优价格。为最优价格。为最优价格。为最优价格。为最优价格。如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如

30、果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该资源。资源。资源。资源。资源。资源。如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表如果某资源的影子价格高于市场价格，表明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力

31、，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该明该资源在系统内有获利能力，应买入该资源。资源。资源。资源。资源。资源。如果某资源的影子价格低于市场价格，表如果某资源的影子价格低于市场价格，表如果某资源的影子价格低于市场价格，表如果某资源的影子价格低于市场价格，表如果某资源的影子价格低于市场价格，表如果某资源的影子价格低于市场价格，表明该资源在系统内无获利能力，应卖出该明该资源在系统内无获利能力，应卖出该明该资源在系统内无获利能力，应卖出该明该资源在系统内无获利能力，应卖出该明该资源在系统内无获利能力，应卖出该明该资源在系统

32、内无获利能力，应卖出该资源。资源。资源。资源。资源。资源。如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对

33、偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源如果某资源的对偶解大于零，表明该资源在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。在系统内有获利能力，应买入该资源。如果某资源的对偶解小于零，表明该资源如果某资源的对偶解小于零，表明该资源如果某资源的对偶解小于零，表明该资源如果某资源的对偶解小于零，表明该资源如果某资源的对偶解小于零，表明该资源如果某资源的对偶解小于零，表明该资源在系统内无获利能力，应卖出该资源。在系统内无获利能力，应卖出该资源。在系统内无获利能力，应卖出该资源。在系统内无获利能力，应卖出该资源。在系统内无获利能力，应卖出该资源。在系统内无获利能力，应卖出该资源。