Play around a bit with those multipliers to reach:
Max(xyz) =
for: {x,y,z} =
Use Lagrange multipliers to find the maximum and minumum values of the function subject to the given constraint
I've gotten the system of equations. (shown above) I'm just not sure how to go about tackling this one. Any words of wisdom from someone more clever would be appreciated
Can you expand a bit on what you mean by "play around", please? Something more to go on? I've been playing around off and on this afternoon and so far am seeing little progress. That is the answer in back of book though.
Since a specific value of is not necessary for a solution, I find it is often easiest to eliminate first by dividing one equation by another. Here, I would first rewrite the equations as , , and .
Dividing the first equation by the second, which is the same as . Similarly, dividing the second equation by the third, which is the same as .
The constraint that has to be satisied is and, from the above, we can replace both and by making the equation so that and . With , so that and so that and . That gives a total of eight points that should be checked for max and min values.