Determine the maximum value of $Z = 11x + 7y$ subject to the constraints$2x + y \le 6,x \le 2,x \ge 0,y \ge 0$

We have the following conditions as per the question,

maximise $Z = 11x + 7y$ …….(i)

Subject to the constraints $2x + y \le 6$ ……..(ii)

$x \le 2$ …….(iii)
$x \ge 0,y \ge 0$ .... (iv)

We see that, required area is the shaded region determined by the system of constraints (ii) to (iv) is OABC and is bounded.

So, now we can use corner points to determine the maximum value of Z.

Hence, the maximum value of Z is 42 at (0,6) .