Suppose you are enclosing a rectangular area to create a rabbit cage. You have 80 ft of fence and want to build a pen with the largest possible area for your rabbit, so you build the cage using an existing building as one side.
a. Make a table showing the areas for some selected values of x, and write a function that gives the area, y, as a function of the width, x.
b. What width maximizes the area? What is the maximum area?