JBMO-SL 2015 A1

MLD

Let $x, y, z$ be real numbers, satisfying the relations

$$\left\{\begin{array}{l} x \geq 20 \\ y \geq 40 \\ z \geq 1675 \\ x+y+z=2015 \end{array}\right.$$

Find the greatest value of the product $P=x \cdot y \cdot z$.