Which is true of $Z = 3x + 5y$ over the region $x + y \ge 2$, $x \ge 0$, $y \ge 0$?

Explanation

1. 01

   The corners are $(2, 0)$ and $(0, 2)$, where $Z = 6$ and 10. The half-plane $3x + 5y < 6$ holds no feasible point, so 6 is the minimum.

2. 02

   The region is unbounded upward: $(100, 0)$ gives $Z = 300$, so there is no maximum.