Maximise $Z = 2x + 2y$ subject to $x + y \le 5$, $x \ge 0$, $y \ge 0$. How many optimal solutions are there?

Explanation

1. 01

   At the corners $(0, 0)$, $(5, 0)$ and $(0, 5)$, $Z = 0$, 10 and 10: the maximum 10 is reached at two corners.

2. 02

   Then every point of the edge joining them gives $Z = 2(x + y) = 10$ as well, so there are infinitely many optimal solutions.