What is the maximum value of $Z = 3x + 4y$ subject to $x + y \le 10, x + 3y \le 18, x \ge 0, y \ge 0$?

Explanation

1. 01

   The corner points of the feasible region are $(0, 0)$, $(0, 6)$, $(6, 4)$, $(10, 0)$.

2. 02

   Values of $Z$: $0$ at $(0, 0)$, $24$ at $(0, 6)$, $34$ at $(6, 4)$, $30$ at $(10, 0)$.

3. 03

   The region is bounded, so the maximum is the largest of these: $34$, at $(6, 4)$.