I have a nasty function that is simplified from an even nastier function:
$F(x,y,z,\lambda) = \frac{-0.0129x-0.0051y-0.0066z}{\sqrt{.44^2x^2 + .15^2y^2 + .44^2z^2 + 0.05808xy + .139392xz - 0.00528yz}} + \lambda (x+y+z-1) $
I am trying to use the Lagrangian to find the max value of $F$ while holding $x + y + z =1$. Hoping to get some kind of guidance on this as it's far above anything I have practised before.