Hi :)  I need to minimize the function 4*z^2 + 2xy + 3yz + 4xz under the following two constraints: 1) xyz = 80 2) y >= 2x Also, x,y,z need to be positive. Please use the lagrangian method. Thank you :)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 4ST
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Hi :) 

I need to minimize the function 4*z^2 + 2xy + 3yz + 4xz under the following two constraints:

1) xyz = 80

2) y >= 2x

Also, x,y,z need to be positive.

Please use the lagrangian method.

Thank you :)

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