Lagrange Multipliers Find 3 positive numbers?

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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 = 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!
 

Answers and Replies

  • #2
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Nevermind, after a major number crunching, I got it. thanks!
 

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