Question

A rectangular pen is built with one side against a barn. if 300 m of fencing are used for the other three sides of the​ pen, what dimensions maximize the area of the​ pen?

Answer 1

Let w= the length of the side perpendicular to the barn 
300-2w= length of the side parallel to the barn
A=w(300-2w)
A=-2w^2+300w
The formula for the w-value of maximum is:
=-b/2a
thus our value will be:
300/4
=75
and
300-2(75)
=150
thus the dimensions to maximize the area is 75 by 150