A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides wont 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 availible for this project and she will use all the wire. what is the maximum area enclosed by the fence then find the maximum of the function ...?

Question

Mathematics

Ozzie

4 May, 12:38

A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides wont 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 availible for this project and she will use all the wire. what is the maximum area enclosed by the fence then find the maximum of the function ...?

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Kristopher Rich · Answer 1

The area enclosed is (2x) (600-2x). (2x) (600-2x) = 1200x-4x2

In order to maximize we need the derivative to be equal to 0. y′=1200-8x=0

1200=8x

x=150

Therefore the sides for maximum area are 150*300.

The area is: 45000