I have posted this problem in the applied math section. Curious to hear what people here would say.
I have a (maybe trivial?) question on constrained optimization. Assume that I have the following maximization problem:
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?
I know that this could mean that the constraint is always non-binding. But what if we changed the constraint to
This clearly has an effect on the problem. So does this mean that the regularity condition (constraint qualification) is violated?