Hi, Dear Math forum users,(adsbygoogle = window.adsbygoogle || []).push({});

I was practicing with my optimization course problem and encountered one type of

Lagrange multiplier question which I have trouble with. I am wondering if anyone could

enlighten me for the following Lagrange problem.

function f = x*y*z subject to 4xy+3yz+2xz = 72

since x y z are lengths, they are all positive.

I set up the Lagrange function:

L = xyz + u*(4xy + 3yz + 2xz - 72)

Differentiate w.r.t x, y, z and u gives:

Lx = yz + u*(4y + 2z)

Ly = xz + u*(4x + 3z)

Lz = xy + u*(3y + 2x)

Lu = 4xy + 3yz + 2xz - 72

Set Lx = Ly = Lz = 0 and solve for x, y, z, and u.

I know that x = y = z = 0 is a trivial solution.

I would like to find x, y, z each in terms of u respectively.

I have tried it on paper many times but still cannot solve it.

Any form of help is appreciated.

Thank you very much

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# Homework Help: Calculation regarding to Lagrange Multiplier

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