VMO 1966 Problem 1

Let $x, y$ and $z$ be nonnegative real numbers satisfying the following conditions: (1) $x + cy \le 36$ ,(2) $2x+ 3z \le 72$ , where $c$ is a given positive number. Prove that if $c \ge 3$ then the maximum of the sum $x + y + z$ is $36$ , while if $c < 3$ , the maximum of the sum is $24 + \frac{36}{c}$ .