A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 ft of fence? What should the dimensions of the garden be to give this area?

Question

A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle.  What is the maximum area that the farmer can enclose with 80 ft of fence?  What should the dimensions of the garden be to give this area?

anonymous · Answer

400 ft. 20 by 20

anonymous · Answer

well I guess I'm wrong actually since he used one side with barn instead of fence..

anonymous · Answer

Assume the length of one side is x, twice of it is 2x, then the other side is (80-2x). The area is 2x(80-2x), which is 160x-4x^2. You take the first derivative and set it equal to 0, which gives 160-8x=0, x=20, and 80-2x=40. So you are pretty much getting a 20*40 garden.