More on optimization problems.

1. sheet metal roof by
flickr user ruthven78
More optimization problems ...
these are them ... conehead by flickr user
greenapplegrenade
the over / under by flickr user churl

2. 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?

3. 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.

7. 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.