Problem

Source: 2021 Bosnia Herzegovina MO p1, posted as TST inside contest collections, 13.6.2021

Tags: algebra, inequalities, max



Let $x,y,z$ be real numbers from the interval $[0,1]$. Determine the maximum value of expression $$W=y\cdot \sqrt{1-x}+z\cdot\sqrt{1-y}+x\cdot\sqrt{1-z}$$