The maximum value of $Z=5x+4y,$ Subject to $y\le 2x,x\le 2y,x+y\le 3,x\ge 0,y\ge 0$ is ..

We have, $z=5x+4y$
Subject to contraints $y\le 2x,x\le 2y,x+y\le 3,x\ge 0,y\ge 0$
On taking given constraints as equations, we get the following3 graph.

Intersecting point of line $y=2x$ and $x+y=3$ is $A\left(1,2\right)$ and intersecting point of line $y=2y$ and $x+y=3$ is $B\left(2,1\right)$
Here OABO is the required feasible region whose corner points are $O\left(0,0\right),A\left(1,2\right)$ and $B\left(2,1\right)$