Question

A factory owner wants to enclose a rectangular area adjoining a factory and then divide it into two smaller areas with a fence parallel to one of the sides, see figure below. No fence is needed a long the factory wall. If a total of 60 meters of fencing is available to enclose the two areas, find the maximum possible total area that can be enclosed. Make sure to show that your answer is the absolute maximum.

Answer 1

Aah, an optimization problem. Nice.
So let's have the width be x and length y. Our figure is now:

Then the are is given by the equation
A(x,y)=x*y