I have a (maybe trivial?) question on constrained optimization. Assume that I have the following maximization problem:

subject to

I setup the Lagrangian and I get the following first order conditions with the lagrange multiplier .

By the Kuhn Tucker conditions, we know that if , then the constraint is binding. However, from the first order conditions, we can see that the multiplier is negative! How can this be? Am I doing things wrong here?

Please help!

Thank you