Question 431927
The perimeter of the pen is 2l + 2w
The area of the pen is l*w
Given: 200 feet of material
So we can write
200 = 2l + 2w -> l + w = 100 -> l = 100 - w
Substitute this value for l in the equation for the area:
A = w(100-w)
This area will be maximized for dA/dw = 0
dA/dw = 100 - 2w
Set=0 and solve for w:
2w = 100 -> w = 50
So the length is also 50.
Therefore, the maximum area = 50*50 = 2500 sq. ft.