(O5) Applied Optimization#
By the end of the lesson you will be able to:
set up and use derivatives to solve applied optimization problems.
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 \(\$ 14\) per linear foot.
The fourth side will use cement blocks, at a cost of \(\$ 28\) 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 \((1,4)\).