- #1
linchien
- 3
- 0
Hi, Dear Math forum users,
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
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