AT-OEMO-BEG 2014 Problem 3

Let $a, b, c$ and $d$ be real numbers with $a < b < c < d$ . Sort the numbers $x = a \cdot b + c \cdot d, y = b \cdot c + a \cdot d$ and $z = c \cdot a + b \cdot d$ in ascending\order and prove the correctness of your result.

(R. Henner, Vienna)