NP-complete
As far as I remember, those are all equivialent. So you make one, you made them all. You already made one ;-)
That thing with limited time and resources is the basic plot of the typical dating sim. There were lots of those in the flash game period. You typically had like 100 days (till prom or whatever) and like 3 stats and girls liking different stats and you needed money to train or go on dates, and could get more money by having more stats and all that. And if you were good at it, you could maybe date more than 1 girl within the time frame. Or achieve the plot device goal at the end of the 100 days as well.
If you did a knapsack dating game, you might want to check out 80 Days. That's a traveling salesman, knapsack and dating sim adventure.
As a game idea: wedding planner. You need to plan seat arrangements. If you are clever enough, you end up nudging your love interest away from your competition and towards spending time with you. Of course you lose your task for the next wedding in that circle of people, if you do bad. And maybe you can nudge your competitors to other people, so not only you have less competition, but also more weddings to plan.
I am not sure which np problem that is. Maybe one of those where you color things.