Carol has 2,000 ft of fencing to fence in a rectangular horse corral. x 1000 -

Algebra
Tutor: None Selected Time limit: 1 Day

Carol has 2,000 ft of fencing to fence in a rectangular horse corral.
x1000 - x
(a) Find a function that models the area A of the corral in terms of the width x of the corral. 
A(x) =

(b) Find the dimensions of the rectangle that maximize the area of the corral. 
width     ft
length     ft
Jul 8th, 2015

Hello!

If one side (width) of a rectangle is x ft, then the opposite is also x and adjacent sides (length) have length of (2000 - 2x)/2 = 1000-x (as at your picture).

So a) the area A(x) = x*(1000-x) (square fts).

b) A(x) = -x^2 + 1000x = -(x-500)^2 +500^2 <= 500^2.
Therefore A(x) has a maximum at x=500(ft). Width=500ft and length=1000-500=500ft.

Please ask if anything is unclear.
Jul 8th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Jul 8th, 2015
...
Jul 8th, 2015
Mar 28th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer