Maximum value of a product How to write the number $60$ as $\displaystyle\sum^{6}_{i=1} x_i$ such that $\displaystyle\prod^{6}_{i=1} x_i$ has maximum value?

Thanks to everyone :)
Is there a way to solve this using Lagrange multipliers?

(of course the $x_i$ must be positive, otherwise the product may be as great as you want)
Hint: if you have $x_i \ne x_j$, substitute both with their arithmetic mean.
