SOLUTION: A farmer wants to build a pen with one side attached to his barn. He has 800metres of fencing. What is the max area that the pen can be? p = 2L + W 800 = 2L + W W = 800 - 2L

Algebra ->  Rectangles -> SOLUTION: A farmer wants to build a pen with one side attached to his barn. He has 800metres of fencing. What is the max area that the pen can be? p = 2L + W 800 = 2L + W W = 800 - 2L       Log On


   

Question 416512: A farmer wants to build a pen with one side attached to his barn. He has 800metres of fencing. What is the max area that the pen can be?
p = 2L + W
800 = 2L + W
W = 800 - 2L

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
This is an optimization problem requiring derivatives. You are on the right track.
The next step is to maximize the area
A+=+L%2AW+=+%28800-2L%29%2AL+=+800L+-+2L%5E2
Now take the derivative and set = 0
dA%2FdL+=+0+=+800+-+4L
Solving for L gives L = 200 m
And W = 800 - 2L -> W = 400 m
So the max. area = A = L*W = 200*400 = 80000 m^2