The maximum value of the objective function $Z=4x+3y$ subject to $4x+2y\le 12$, $2x+4y\ge 6$, $x\ge 0,y\ge 0$ is:

Plotting the constraints:$4x+2y=12⟹$ points $(3,0)$ and $(0,6)$.$2x+4y=6⟹$ points $(3,0)$ and $(0,1.5)$.Corner points of the feasible region are $(3,0)$, $(0,6)$, and $(0,1.5)$.Calculate $Z=4x+3y$ at these points:At $(3,0)$: $Z=4(3)+3(0)=12$ At $(0,6)$: $Z=4(0)+3(6)=18$ At $(0,1.5)$: $Z=4(0)+3(1.5)=4.5$ The maximum value is 18.