Use Lagrange multipliers to find the max and min values of the function subject to the given constraints.

I get multiple answers for , which is my problem.

function:

subject to:

and

Now I set them equal to solve for using all of the possible combinations, here is where my answers get messed up. They are all different, and makes no sense.

From here any solution i pick does not give me the solution of as a max. Also is the min.

Any help is appreciated as always.

Thanks!