第10周lingo软件使用的练习题

第10周lingo 软件使用的练习题

1. 用傻瓜式输入法求解优化问题

⎪⎪⎩⎪⎪⎨⎧≤≥=----≥++≤++-+-+=无约束

4321432143243214

321,,0,02

47325433432..4323min x x x x x x x x x x x x x x x t s x x x x f min =3*x1+2*x2-3*x3+4*x4;

x1-2*x2+3*x3+4*x4<3;

x2+3*x3+4*x4>-5;

2*x1-3*x2-7*x3-4*x4=2;

x1>0;

-x2>0;

@free (x3);

@free (x4);

end

Global optimal solution found.

Objective value: -9.500000

Infeasibilities: 0.000000

Total solver iterations: 2

Variable Value Reduced Cost X1 0.000000 0.000000 X2 0.000000 4.000000 X3 0.7500000 0.000000 X4 -1.812500 0.000000

Row Slack or Surplus Dual Price 1 -9.500000 -1.000000 2 8.000000 0.000000 3 0.000000 -2.500000 4 0.000000 -1.500000 5 0.000000 0.000000 6 0.000000 0.000000

2. 利用lingo 软件的“段”编程求解下面背包问题：

设有n=8个体积分别为54，45，43，29，23，21，14，1的物体和一个容积为C=110的背包，问选择哪几个物体装入背包可以使其装的最满。

sets:

s/1..8/:v,x;

endsets

data:

v=54,45,43,29,23,21,14,1;

enddata

max=@sum(s(i):v(i)*x(i));

@sum(s(i):v(i)*x(i))<110;

@for(s(i):@bin(x(i)));

end

Global optimal solution found.

Objective value: 110.0000

Objective bound: 110.0000

Infeasibilities: 0.000000

Extended solver steps: 0

Total solver iterations: 0

Variable Value Reduced Cost V( 1) 54.00000 0.000000 V( 2) 45.00000 0.000000 V( 3) 43.00000 0.000000 V( 4) 29.00000 0.000000 V( 5) 23.00000 0.000000 V( 6) 21.00000 0.000000 V( 7) 14.00000 0.000000 V( 8) 1.000000 0.000000 X( 1) 0.000000 -54.00000 X( 2) 1.000000 -45.00000 X( 3) 1.000000 -43.00000 X( 4) 0.000000 -29.00000 X( 5) 0.000000 -23.00000 X( 6) 1.000000 -21.00000 X( 7) 0.000000 -14.00000 X( 8) 1.000000 -1.000000

Row Slack or Surplus Dual Price

1 110.0000 1.000000

2 0.000000 0.000000