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July 31, 2014

July 31, 2014

Posted by **Chris** on Friday, December 16, 2011 at 5:54am.

why is X along the road sqrt2/2?

] A rancher plans to set aside a rectangular region of one square kilometer for cattle and wishes to build a wooden fence to enclose the region. Since one side of the region will run along the road, the rancher decides to use a better quality wood for that side which costs three times as much as the wood for the other sides. What dimensions will minimize the cost of the fence?

x y = 1

c = 3 x + x + 2 y = 4 x + 2 y

c = 4 x + 2/x

dc/dx = 4 - 2/x^2

= 0 for minimum

4 = 2/x^2

x^2 = 1/2

x = 1/sqrt 2 = sqrt 2/2 along road

y = sqrt 2

- calculus -
**drwls**, Friday, December 16, 2011 at 6:13amThis question has already been answered by Damon

- calculus -
**Chris**, Friday, December 16, 2011 at 6:16amYes, I know, but I i had question about the answer... I'm math stupid :)

- calculus -
**Damon**, Friday, December 16, 2011 at 8:37amThe smaller of x or y will be the expensive fence along the road.

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