Solution 1:

Drawing, we can see that the interval given by this problem is not a closed interval, that is, it is not feasible.

Both downward and right can be extended indefinitely, so there is no maximum.

Solution 2:

Let 2x+y=a(x+4y)+b(3x+5y).

You can get A=- 1 and b= 1.

Namely z=2x+y=(3x+5y)-(x+4y)

While x+4y ≤-3 and 3x+5y < 25.

So z has no maximum.