Solve the following linear programming problem graphically: Maximise Z =20 x +30 y Subject to the constraints: x + y ≤ 80; 2 x +3 y ≥ 100; x ≥ 14; y…

Solve the following linear programming problem graphically : Maximise $\displaystyle \mathrm{Z}=20 \mathrm{x}+30 \mathrm{y}$ Subject to the constraints : \[\begin{aligned} & \mathrm{x}+\mathrm{y} \leq 80 \\ & 2 \mathrm{x}+3 \mathrm{y} \geq 100 \\ & \mathrm{x} \geq 14 \\ & \mathrm{y} \geq 14 \end{aligned} \]