How Long Should I Hold The Door Open?

Economists like to weigh the benefits and costs of an activity to find the optimal amount of time that should be spent on it.  While entering the Community Y this morning, I held the door open for a man entering behind me.  I wondered if I would have held the door open if the man would have been farther behind me.  I calculated my utility function as a constant 2 utils, and my cost function as .5X^3.  I immediately plotted the the two and derived the graph you see.  As you can see, I won't wait long.

I wrote this post as a way for my students to see marginal decision making.  I want them to make something like it to make their learning relevant.

Some other ideas are how long should you study, workout, watch television, and write a blog post.