# Inspired by Lakshya Sinha

Algebra Level 4

Find the minimum value $$m$$ and the maximum value $$M$$ of $f(x,y,z)=x^3+\frac{y^3}{4}+\frac{z^3}{9}$ when $$x+y+z=12$$, where $$x,y$$ and $$z$$ are non-negative real numbers. Enter $$m+M$$.

×