Solve the following linear programming problem graphically: Maximise z =5 x +4 y subject to the constraints x +2 y ≥ 4; 3 x + y ≤ 6; x + y ≤ 4; x, y…

Solve the following linear programming problem graphically : Maximise $\displaystyle \mathrm{z}=5 \mathrm{x}+4 \mathrm{y}$ subject to the constraints \[\begin{aligned} & \mathrm{x}+2 \mathrm{y} \geq 4 \\ & 3 \mathrm{x}+\mathrm{y} \leq 6 \\ & \mathrm{x}+\mathrm{y} \leq 4 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \]