What is the minimum value of $Z = x + 2y$ subject to $2x + 3y \le 12, x + y \ge 2, x \ge 0, y \ge 0$?

Explanation

1. 01

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

2. 02

   Values of $Z$: $4$ at $(0, 2)$, $8$ at $(0, 4)$, $2$ at $(2, 0)$, $6$ at $(6, 0)$.

3. 03

   The region is bounded, so the minimum is the smallest of these: $2$, at $(2, 0)$.