Lagrange Multipliers Find 3 positive numbers?

[tak13]

Homework Statement

Find 3 positive numbers x, y and z for which: their sum is 24 and which maximizes the product: P = x²y³z. Find the maximum product.

The Attempt at a Solution

Ok, I know how to set up the equations.

x + y + z = 24

Delta(F) <2xy³z, 2x²y²z, x²y³>

fx = 2xy³z = λ
fy = 2x²y²z = λ
fz = x²y³> = λ

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

 

[tak13]

Nevermind, after a major number crunching, I got it. thanks!