Question 318930
I'm assuming these numbers need to be integers.
{{{P=xy^2z}}}
Since y is squared, you want y to be as large as possible. 
The smallest, non-zero value for x and z to have so that y can be maximized is 1.
{{{x=z=1}}}
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{{{x+y+z=32}}}
{{{1+y+1=32}}}
{{{y=30}}}
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{{{Pmax=1*30^2*1=900}}}