What is the minimum value of $Z = 5x + 4y$ subject to $x + 2y \ge 10, 3x + y \ge 15, x \ge 0, y \ge 0$?

Explanation

1. 01

   Corners: $(0, 15)$, $(4, 3)$, $(10, 0)$; $Z$ there is $60$, $32$, $50$.

2. 02

   The region is unbounded, so check that $5x + 4y < 32$ has no point in common with it: the line $5x + 4y = 32$ touches the region only at $(4, 3)$.

3. 03

   So the minimum is $32$.