For $x + 2y \ge 6$, $x \ge 0$, $y \ge 0$, what is the minimum of $Z = x + 3y$?

Explanation

1. 01

   The corners of this unbounded region are $(6, 0)$ and $(0, 3)$, with $Z = 6$ and $Z = 9$.

2. 02

   The half-plane $x + 3y < 6$ has no point in common with the region, so the minimum is 6.