If you do something profitably, two things can be true, and students need both. First, it can mean “in a way that makes a profit”: they sold the land profitably. Second — and this is very common — it can mean “in a useful way, so that you get something good out of it,” even when no money moves. You can spend an afternoon profitably by reviewing notes. You can look at old mistakes profitably. Though actually, the “useful result” sense is older and wider than the money sense, but business writing usually wants the money. The word is a little formal in both uses; friends more often say “It was worth it” or “We made money.”