At which point does $Z = 2x + 3y$ reach its maximum, subject to $x + y \le 7, 2x + y \le 10, x \ge 0, y \ge 0$?

Explanation

1. 01

   Corners: $(0, 0)$, $(0, 7)$, $(3, 4)$, $(5, 0)$.

2. 02

   $Z$ there: $0$, $21$, $18$, $10$; the largest is at $(0, 7)$.