Where did you do it? I am not seeing the work. I'd be glad to help if you can show some progress with this problem.

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- July 21st 2010, 07:43 PM #1

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## Did i do this right

A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

let the sides by x and y. then xy = 500000, so y = 500000/x

the length you want to minimize is f(x) = 3x + 2y (because of the extra bit down the middle)

f(x) = 3x + 1000000/x

to find the optimal length, solve df/dx = 0

df/dx = 3 - 1000000/x^2 = 0

i.e., solve 3 = 1000000/x^2

x^2 = 1000000 / 3

x = 1000 / sqrt(3)

shortest total length is f(1000 / sqrt(3))

= 3000 / sqrt(3) + 1000 sqrt(3)

- July 21st 2010, 07:47 PM #2

- July 21st 2010, 08:05 PM #3

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- July 21st 2010, 08:43 PM #4
The work looks fine. I'd only add a justification that it's a min and not a max. Use the first or the second derivative test to do this. Unless your goal is to get the right answer without worrying too much about fully explaining it.

Good luck!

PS... would also include the units in the final answer.

- July 21st 2010, 10:02 PM #5

- July 22nd 2010, 12:55 PM #6