On cross-intersecting families of sets

A family A of l-element subsets and a family B of k-element subsets of an n-element set are cross-intersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product \A\\B\, and give a new and short proof for one of them. We also determine the maximum of \A\omega(l) + \B\omega(k) for arbitrary positive weights omega(l); omega(k).