Find the maximum value a product Three positive integers their sum is 90, find the numbers for which their product is maximum.
Let the numbers $x,y$ and $z$
we have
$$x+y+z=90$$
Using AM-GM 
$$x+y+z\ge 3(xyz)^{\frac{1}{3}}$$
then
$$xyz\le2700$$
then 
$$xyz=2700$$
Now we have two equations and 3 unknowns can we find those numbers using these two equations ?

HINT
Recall that for AM-GM equality holds for $x=y=z$.
