Related rates problem involving two chicken coops
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Related rates problem involving two chicken coops

[From: ] [author: ] [Date: 11-12-07] [Hit: ]
b.c.d.e.| ........
A farmer has 24 feet of fencing to build a chicken coop, which will be shaped like a rectangle split into two pens. What is the maximum area of the chicken coop?

a. 12
b. 16
c. 18
d. 20
e. 24

-
Shape of chicken coop:

_________
| ...... | ...... |
| ...... | ...... | x
|____|____|
. . . . y

Total fencing = 24 ft
3x + 2y = 24
2y = 24 - 3x
y = 12 - 3/2 x

A = x * y
A = x (12 - 3/2 x)
A = -3/2 x^2 + 12x

A' = -3x + 12 = 0 -----> x = 4
A'' = -3x < 0 for all x

Maximum area when x = 4, y = 6 -----> maximum area = 4 ft * 6 ft = 24 sq. ft

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