Question

用LINGO 编程解一个线性规划问题，不会编，急急急！在线等

Min=6000-290X1-470X2-720X3-1060X4-1490X5;
X1>=1;
X2>=1;
X3>=1;
X4>=1;
X5>=1;
X1-X5都必须为整数

Answer 1

若求最小值，则有无界解，即目标函数没有最小值。程序如下：
Min=6000-290*X1-470*X2-720*X3-1060*X4-1490*X5;
X1>=1;
X2>=1;
X3>=1;
X4>=1;
X5>=1;
@GIN(x1);@GIN(x2);@GIN(x3);@GIN(x4);@GIN(x5);

运行结果为：
Model is unbounded

Variable Value
X1 0.000000
X2 0.000000
X3 0.000000
X4 0.000000
X5 0.000000

Row Slack or Surplus
1 0.000000
2 -1.000000
3 -1.000000
4 -1.000000
5 -1.000000
6 -1.000000

若改为求最大值，则有有界解。程序如下：
Max=6000-290*X1-470*X2-720*X3-1060*X4-1490*X5;
X1>=1;
X2>=1;
X3>=1;
X4>=1;
X5>=1;
@GIN(x1);@GIN(x2);@GIN(x3);@GIN(x4);@GIN(x5);

运行结果为：
Global optimal solution found.
Objective value: 1970.000
Objective bound: 1970.000
Infeasibilities: 0.000000
Extended solver steps: 0
Total solver iterations: 0

Variable Value Reduced Cost
X1 1.000000 290.0000
X2 1.000000 470.0000
X3 1.000000 720.0000
X4 1.000000 1060.000
X5 1.000000 1490.000

Row Slack or Surplus Dual Price
1 1970.000 1.000000
2 0.000000 0.000000
3 0.000000 0.000000
4 0.000000 0.000000
5 0.000000 0.000000
6 0.000000 0.000000

Answer 2

这个为无界解，把min改成max就有解了

model:
min=6000-290*X1-470*X2-720*X3-1060*X4-1490*X5;
X1>=1;
X2>=1;
X3>=1;
X4>=1;
X5>=1;
@gin(X1);
@gin(X2);
@gin(X3);
@gin(X4);
@gin(X5);
end