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
a. 12
b. 16
c. 18
d. 20
e. 24
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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
Mαthmφm
_________
| ...... | ...... |
| ...... | ...... | 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
Mαthmφm