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March 11, 2014

# Homework Help: preculculus

Posted by By Lana on Wednesday, October 26, 2011 at 7:24am.

27. A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides won't require fencing). She has decided to create a rectangular shape for the area, and will use barbed wire to create the enclosure. There are 600 feet of wire available for this project, and she will use all the wire. What is the maximum area that can be enclosed by the fence? (Hint: Use this information to create a quadratic function for the area enclosed by the fence, then find the maximum of the function.)

• preculculus - Reiny, Wednesday, October 26, 2011 at 8:44am

let the width be x ft
let the length be y ft, (only one of those needed)
y + 2x = 600
y = 600-2x

Area = xy = x(600-2x)
= -2x^2 + 600x

complete the square,
-2(x^2 - 300x + 22500 - 22500)
= -2(x-150)^2 + 45000

Max area is 45000 ft^2 when x = 150 and y = 300

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