Question: Consider the problem max xy subject to x + y = 2. Show that (x, y) = (1, 1), with λ = 1, is the only solution of the first-order conditions. (That this is indeed the solution of the problem is easily seen by reducing it to the one-variable problem of maximizing xy = x(2 - x).) But (1, 1) does not maximize the Lagrangian L(x, y) = xy - 1 · (x + y - 2). Why not?