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

(D) We have to maximize $Z=11 x+7 y$ subject to the constraints:
$2 x+y \leq 6$
$x \leq 2$
$x \geq 0, y \geq 0$
The feasible region is bounded by the lines $2x+y=6$,$x=2$,$x=0$,and $y=0$. The corner points of the shaded region are $O(0,0)$,$A(2,0)$,$B(2,2)$,and $C(0,6)$.

Corner Point	Value of $Z = 11x + 7y$
$O(0,0)$	$11(0) + 7(0) = 0$
$A(2,0)$	$11(2) + 7(0) = 22$
$B(2,2)$	$11(2) + 7(2) = 22 + 14 = 36$
$C(0,6)$	$11(0) + 7(6) = 42$

Comparing the values of $Z$ at all corner points,the maximum value is $42$ at the point $(0,6)$.