SOLUTION: A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. Find the dimensions of the fence to maximize the area enclosed by the fe

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Question 252341: A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. Find the dimensions of the fence to maximize the area enclosed by the fence.

Found 2 solutions by stanbon, rfer:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. Find the dimensions of the fence to maximize the area enclosed by the fence.
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Draw the picture.
You have a rectangle with one side being the river.
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Let each side perpendicular to the river be "x".
Then the side parallel to the river is "2400-2x".
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Area = width*length
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A(x) = x(2400-2x)
A(x) = 2400x - 2x^2
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You have a quadratic with a = -2 and b = 2400
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Maximum Area occurs where x = -b/2a = -2400/(2*-2) = 600 ft. (width)
length = 2400-2x = 2400-2*600 = 1200 (length)
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Cheers,
Stan H.

Answer by rfer(16322) (Show Source):
You can put this solution on YOUR website!