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

Explanation

1. 01

   The corner points of the feasible region are $(0, 3)$, $(0, 5)$, $(3, 0)$, $(4, 3)$, $(5, 0)$.

2. 02

   Values of $Z$: $15$ at $(0, 3)$, $25$ at $(0, 5)$, $6$ at $(3, 0)$, $23$ at $(4, 3)$, $10$ at $(5, 0)$.

3. 03

   The region is bounded, so the minimum is the smallest of these: $6$, at $(3, 0)$.