TITLE: Interesting, unusual max/min problems?
QUESTION [6 upvotes]: So I've got to that stage of my elementary mathematics subject for engineers when we talk about differentiation and solution of max/min problems.  And I'd like to entertain and engage the students with some interesting problems.  Pretty much every book and website talks about maximizing rectangular areas of land with fences of a given length, or maximizing the volume of a box with square cross section (and given surface area) etc.  No student is ever excited by these.  Slightly more interesting is the problem of maximizing the length of a pipe (considered as having zero cross section) which can be manoeuvred around a right-angled hallway.  There must be more interesting problems, or at least, more interesting ways to dress up these problems.  
But I don't know of any, and would be delighted to know of some!

REPLY [2 votes]: Two books; I guess yesterday, somebody asked again about the question of Regiomantus, Finding the widest angle to shoot a soccer ball from the sideline using optimization!! 
I knew of this from some book i had 40 years ago, but it is in two books that can be purchased (or borrowed) , Heinrich Dorrie (translated) 100 Great Problems of Elementary Mathematics with a cozen problems in the final chapter, called Extremes. Andre recommended Ivan Niven, Maxima and Minima without Calculus; I am having trouble seeing whether that is still in print...