I know you're talking about real life rather than puzzles, but you may well be interested in, and enjoy solving, the class of puzzles which are purely about optimisation. See http://www.otuzoyun.com/puzzledesign/index.html and the puzzles submitted for previous years' competitions.

As to how to go about solving a general optimisation puzzle, er... beats me!

*deliberately ignores the interesting questions in your last para*