What is the maximum value of $Z = 4x + 3y$ subject to $x + y \le 6, 2x + y \le 8, x \ge 0, y \ge 0$?

Explanation

1. 01

   The corner points of the feasible region are $(0, 0)$, $(0, 6)$, $(2, 4)$, $(4, 0)$.

2. 02

   Values of $Z$: $0$ at $(0, 0)$, $18$ at $(0, 6)$, $20$ at $(2, 4)$, $16$ at $(4, 0)$.

3. 03

   The region is bounded, so the maximum is the largest of these: $20$, at $(2, 4)$.