Question

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.)

Answer 1

you can express the perimeter as 2W + L = 600 (since there are only 3 sides of fence used)

area = W*L

use the first equation to re-write area in terms of one variable (L or W) and then solve for that variable

Answer 2

so, let's just solve for L

L = 600 - 2W

then area becomes W*L = W*(600-2W)

then expand using foil and find the maximum using the formula we used before (x, or in this case, W = -b/(2a)

Answer 3

so w=-600/(2*2)

Answer 4

b and a are not 600 and 2

keep in mind you have to re-write the equation in standard form to find a, b, c

so expand W*(600-2W) using foil

Answer 5

wait so what are the two binomials that i will use to foil

Answer 6

should be the distributive property actually

Answer 7

A(B-C) = A*B - A*C

W*(600-2W) = ?

Answer 8

600w-600(2)

Answer 9

W*2W = ?

Answer 10

w^2

Answer 11

:/

Answer 12

don't forget the 2

W*2W = 2*W*W = 2W^2

Answer 13

so the entire function is

-2W^2 + 600W

making W = -b/(2a) = -600/(2*(-2)) = 150

W = 150

now, find L using the formula from before L = 600 - 2W

then after that, find area = L*W

Answer 14

l=300

Answer 15

good, now find area using W*L

Answer 16

300*150=45000

Answer 17

good, that's your answer, 45,000 ft ^2