> It's amazing how often someone finds an NP-Complete problem and doesn't even attempt to try and solve it.

Just out of curiosity, how are you coming across these? I've dabbled in integer programming with both Gurobi and SAS (once for hobby purposes, and twice to solve some pretty major problems for work). For some reason, I've found it to be some of the most enjoyable work I've done to date - perhaps because of the satisfaction of being able to say "this is (one of) the best possible solution(s) to this problem."

I'm constantly looking for new problems to play around with (particularly those with business applications), but I don't find too many. In fact, just yesterday, I was commuting home running through business models and trying to imagine likely unsolved problems where you'd be minimizing/maximizing something subject to constraints...