MathNet 2009-part-01 — 175 problems (EN–VI) Question 140

Let $f(x, y, z) = \frac{x(2y-z)}{1+x+3y} + \frac{y(2z-x)}{1+y+3z} + \frac{z(2x-y)}{1+z+3x}$, where $x, y, z \ge 0$, and $x+y+z = 1$. Find the maximum value and the minimum value of $f(x, y, z)$. (Posed by Li Shenghong)