Setting and is...
Now what You have to do is to find the values of and [with the condition , Lagrange's multipliers ...] so that (1) is maximized...
Q: For fixed find the value of that is maximized when .
A: Well, I would think I need to find the the roots to the equation firs. After that I am not sure. Since this is a max question, I feel that I need to take the derivative at some point with respect to z.
Any help would be appreciated.