CAPS 2002 Problem 2

A triangle $ABC$ has sides $BC = a, CA = b, AB = c$ with $a < b < c$ and area $S$ . Determine the largest number $u$ and the least number $v$ such that, for every point $P$ inside $\triangle ABC$ , the inequality $u \le PD + PE + PF \le v$ holds, where $D,E, F$ are the intersection points of $AP,BP,CP$ with the opposite sides.