Example 1#

Example 2#

Example 3#

Example 4#

Helpful Geometry#

Example 1#

You want to plant a rectangular garden along one side of a house, with a fence on the other three sides.

Find the dimensions of the largest garden that can be enclosed using $40$ feet of fencing.

Example 2#

The manager of a retail store wants to build a $600$ sq ft rectangular enclosure on the store’s parking lot.

• Three sides will use redwood fencing, at a cost of $\mathrm{\$}14$ per linear foot.

• The fourth side will use cement blocks, at a cost of $\mathrm{\$}28$ per linear foot.

Find the dimensions of the enclosure that will minimize the total cost of the building materials.

Example 3#

A closed box is to be constructed so that it has a square base and encloses 1000 cubic centimeters of space.

Find the dimensions that minimize the surface area of the box.

Example 4#

Find the point on the parabola $y^2=2x$ that is closest to the point $(1,4)$.