Quadratic functions

Question

A farmer wants to build a pen against a side of mountain. He has 200 feet of fencing. what is the maximum area he can enclose? What are the dimensions of his own of maximum area?

Answer 1

Assuming that the pen is rectangular, 

 

Let x = length of side parallel to the mountain

     y = length of each of the other 2 sides

 

Then, x+2y = 200    So, x = 200-2y

 

Area = xy = (200-2y)(y)

 

               = -2y² + 200y

 

Maximum area when y = -200 / [2(-2)] = 50 ft

 

                               x = 200 - 2y = 100 ft

 

Maximum area = xy = (100)(50) = 5000 ft²