Question 888586
A farmer wants to fence in three sides of a rectangular field with 1000 feet of fencing. The other side of the rectangle is a river. If the enclosed area is to be maximum, find the dimensions of the field.
Sides perpendicular to the river:: x ft
Side parallel to the river:: 1000-2x
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Area of the rectangle: 
A = x(1000-2x) = 1000x - 2x^2 sq ft
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To maximize Area::
A' = -4x + 1000
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Solve:: -4x + 1000 = 0
x = 250 ft (length of side perpendicular to the river)
1000-2x = 500 ft. (length of the side parallel to the river)
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Area = 250*500 = 125,000 sq ft
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Cheers,
Stan H.
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