MATH 221 Exercises on Optimization

Solve any two of the following problems:

1. Find the maximum area of a rectangle whose base is on the x-axis and whose other two vertices are on the graph of y = 8 – x².

2. Find the point (x,y) in the first quadrant on the line 4x+3y-12 = 0 such that the rectangle two of whose sides are on the x and y axes and whose other vertex is at (x,y) has maximum area.

3. A farmer wishes to build a pasture as pictured below. What is the minimum length of fence he needs if the total area of the fenced in region is 30,000 square feet?

4. Find the point (or points) on the graph of that is closest to (0,0).