More optimizations problems ...

... these are them.

Sheet Metal Roof

highway bridge.

Conehead

Dory Reflection- 733AM

Wire and Wheat

Let's start with ...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?

and another ...A North-South highway intersects an East-West highwat 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.

This one's short ...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 cone coincide.