KöMaL 2009 B4170

A plane intersects the edges $AB$, $BC$, $CD$ and $AD$ of a tetrahedron ABCD at points $K$, $L$, $M$ and $N$, respectively. Prove that $\frac{AK}{AB} \cdot \frac{BL}{BC} \cdot \frac{CM}{CD} \cdot \frac{DN}{AD} \le \frac{1}{16}$.