Hello. I am trying to teach myself the Lagrangean method for purposes of constrained optimization, and I've had a couple of shots at a problem which I, uh, haven't been able to solve for some reason. Mostly because it degenerates to algebraic nonsense, I think. I would appreciate if someone took a look at the first part of my solution, so I can be sure that I am not messing it up before I start solving the equation system it yields, which obviously can be messed up easily.
I have an objective function (which is to be minimized)
and a constraint function
I make a Lagrangean:
which obviously turns into
and I proceed taking partial derivatives, putting them equal to zero and thus creating a system of equations:
Is there anything obviously messed up so far? When I put the system of equations into CAS, it gives "false" as solution, so I kind of guess that I am messing something up.