Question 31
Let $x$, $y$, $z$ and $w$ be nonnegative real numbers such that $x + y + z + w = 1$. Find the greatest and least value of the expression
$$
(x + 3y)(y + 2z) + (y + 3z)(z + 2w) + (z + 3w)(w + 2x) + (w + 3x)(x + 2y).
$$
$$
(x + 3y)(y + 2z) + (y + 3z)(z + 2w) + (z + 3w)(w + 2x) + (w + 3x)(x + 2y).
$$