Larry has 300 meters of fencing material with which to build a rectangular pen with a partition running down the middle. One side of the pen is an existing long straight wall. The middle partition is perpendicular to the wall. Find the dimensions of the pen which encloses the maximum area.

A length of wire that is 160 cm long is cut into two pieces: one to form an equilateral triangle and the other to form a circle. Where do you cut the wire to makes shapes that enclose a maximum amount of area for the two shapes? Where do you cut the wire to enclose a minimum amount of area for the two shapes?

A framer has 160 feet of fencing to enclose two adjacent rectangular pens. what dimensions should he use for the length and width of each pen so that total area enclosed is a maximum?