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1 October, 16:52

Farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a straight river. he needs no fence along the river. write the function that will produce the largest area if x is the short side of the rectangle.

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  1. 1 October, 17:00
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    Let each side perpendicular to the river be "x".

    Then the side parallel to the river is "2400-2x".

    The function would be:

    A (x) = x (2400-2x)

    And it would be: A (x) = 2400x - 2x^2

    To solve the equation:

    You have a quadratic with a = - 2 and b = 2400

    Maximum Area happens where:

    x = - b/2a

    = - 2400 / (2*-2)

    = 600 ft. (width)

    To find the length it will be:

    = 2400-2x = 2400-2*600 = 1200 (length)
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