Lagrange Multiplier

  • Thread starter Oglethorpe
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  • #1
Find the maximum value of f(x,y,z) = 5xyz subject to the constraint of [PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP9619f6019f3fia87i60000567g3gb3dhi833if?MSPStoreType=image/gif&s=6&w=126&h=20. [Broken]

I know to find the partial derivatives of the function and the constraint. Then, set up f(x)=λg(x) and so forth for each partial. Everything else is beyond me...
 
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Answers and Replies

  • #2
Greetings! Correct, then use your constraint, g(x), to give you the fourth equation. In other words, your equations will be:
fx = λ gx,
fy = λ gy,
fz = λ gz, and
g(x).
With four equations and four unknowns, you should be able to solve.
 
  • #3
HallsofIvy
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By the way, since the value of [itex]\lambda[/itex] itself is not part of the answer needed, you may find it simplest to start by eliminating [itex]\lambda[/itex] by dividing one equation by another.

(I would not say that you set [itex]f(x)= \lambda g(x)[/itex]. Rather you set [itex]\nabla f(x)= \lambda \nabla g(x)[/itex].)
 

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