Inequalities problem

[Primarygun]

Given, [Math]S=x^{3}y^{2}z[/Math]

and [Math]x+y+z=1[/Math]

Determine the greatest value of S.

How do we start this type of question?

I started with

[Math]S=xxxyyz[/Math] where there are six terms;

used AM-GM and found that x=y=z, I know it's wrong, but why?

Then I think it occurs because there's no limits of them.

Therefore, I sub [Math]z=1-x-y[/Math]

So [Math]S=(1-x-y)(x^{3}y^{2})[/Math]

But there's no clear solution for me.

What should I do next?

[CanadaAotS]

you must be missing an equation. I'm sure with 3 variables you'd need 3 equations...

 

EDIT: nvr mind if you had 3 equations it wouldnt be inequality, you'd just solve it -_-' lol