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What is the least amount of fencing that will be needed?
Farmer Jones wants to fence off a rectangular area next to the wall of his to use as a garden. The garden is to have an area of 5000 square yards and is to be fenced off on three sides not adjacent to the house.
Answer: Assume the two identical sides of fencing are x yards, the third side opposite the wall is (5000/x) yards
So the perimeter is 2x+(5000/x) yards
Take the derivative of 2x+(5000/x), and we get 2+5000(-x^-2) = 2 - 5000(x^-2)
The minimum occurs at 2 - 5000(x^-2) = 0, solve for x:
5000(x^-2) = 2
(x^-2) = 1/2500
x^2 = 2500
x = 50 or -50 (not possible)
So, x = 50
The least amount of fencing is 50+50+(5000/50)=200 yards
