This normally wouldn't be so hard for me, except for the awkward constraint we've been given.

Find the maximum and minimum values of the function

when is a point in the set

.

I've been told that using Lagrange Multipliers is the proper method to solve this, but I'm not so sure. I'm new to using Lagrange Multipliers, and I haven't seen a question for which the constraint is a set that doesn't have a definite value.