Question
A rancher has 900 meters of fence to enclose a rectangular corral. The corral is to be divided into four subcorrals. What are the overall dimensions of the large enclosure that yield the maximum area?
Answers
let the width of each smaller enclosure be x
let the length of each smaller enclosure be y
So 8x + 2y = 900
y = 450 - 4x
Large area = A = 4xy
= 4x(450-4x)
= 1800x - 16x^2
dA/dx = 1800 - 32x
= 0 for a max of A
32x = 1800
x = 56.25 and y = 450 - 4(56.25) = 225
So the large enclosure is 4x by y
or 225 by 225
(no surprise that the large field would be a square, usually this type of question has one side against a barn or a river)
let the length of each smaller enclosure be y
So 8x + 2y = 900
y = 450 - 4x
Large area = A = 4xy
= 4x(450-4x)
= 1800x - 16x^2
dA/dx = 1800 - 32x
= 0 for a max of A
32x = 1800
x = 56.25 and y = 450 - 4(56.25) = 225
So the large enclosure is 4x by y
or 225 by 225
(no surprise that the large field would be a square, usually this type of question has one side against a barn or a river)
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