Question

设变量x,y满足约束条件y>=0。x-y+1>=0。x+y-3<=0,求目标函数z=2x+y的最大值

Answer 1

画图，在（3,0）点处取最大值，代入z=2x+y得6

Answer 2

可以用lingo求解，代码如下：
max=2*x+y;
y>=0;
x-y+1>=0;
x+y-3<=0;
结果为：
Global optimal solution found.
Objective value: 6.000000
Infeasibilities: 0.000000
Total solver iterations: 1

Variable Value Reduced Cost
X 3.000000 0.000000
Y 0.000000 1.000000

Row Slack or Surplus Dual Price
1 6.000000 1.000000
2 0.000000 0.000000
3 4.000000 0.000000
4 0.000000 2.000000