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## Homework Statement

Find 3 positive numbers x, y and z for which: their sum is 24 and which maximizes the product: P = x

^{2}y

^{3}z. Find the maximum product.

## The Attempt at a Solution

Ok, I know how to set up the equations.

x + y + z = 24

Delta(F) <2xy

^{3}z, 2x

^{2}y

^{2}z, x

^{2}y

^{3}>

fx = 2xy

^{3}z = λ

fy = 2x

^{2}y

^{2}z = λ

fz = x

^{2}y

^{3}> = λ

Substitution part is where I am stuck. Any helps would be awesome! Thanks!