More optimization problems ... these are them ...

sheet metal roof by flickr user ruthven78

the over / under by flickr user churl

conehead by flickr user greenapplegrenade

A long rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides so that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?

A North-South highway intersects an East-West highway at a point P. A car crosses P at 10:00 am, traveling east at a constant speed of 20 mi/hr.At that same instant another car is 2 miles north of P, traveling south at 50 mi/hr. Find the time at which they are closest to each other and approximate the minimum distance between the automobiles.

Find the maximun volume of a right circular cylinder that can be inscribed in a cone of altitude 12 centimeters, and base radius 4 centimeters, if the centres of the cylinder and cond coincide.