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September 23, 2014

September 23, 2014

Posted by **Chris** on Friday, December 16, 2011 at 5:26am.

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?

You answered:

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

Now I have a stupid question... what happened to the y in the c= equations?

- Calculus -
**Damon**, Friday, December 16, 2011 at 5:30amx y = 1

so

y = 1/x

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