The shaded region in the figure is the feasible region for x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.

Explanation

1. 01

   The corner points of the feasible region are $(0, 0)$, $(0, 4)$, $(2, 3)$, $(4, 0)$.

2. 02

   Values of $Z$: $0$ at $(0, 0)$, $20$ at $(0, 4)$, $23$ at $(2, 3)$, $16$ at $(4, 0)$.

3. 03

   The region is bounded, so the maximum is the largest of these: $23$, at $(2, 3)$.