I am a student who would like to become a teacher, so I am currently following courses in education. One of the things I learned, is that students like authentic, realistic problems. However, much of the extremum problems (in one variable) appear very 'fabricated'. I only know a few 'realistic extremum problems':
- minimizing some cost function
- maximizing some return function
- maximizing the volume of a box.
A realistic example of the third problem can be found here, where the volume of a box is maximized. This box is the kind of box you receive a package in: it is closed, with overlapping flaps.
With respect to multivariable functions, I can think of one extra example: determining a regression line.
However, this list seems rather short. Can anyone give extra examples of real-life situations where we wish to maximize/minimize some sort of function? (For my class, single variable functions are the most interesting, but I equally like multivariable examples.)