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28 January, 18:29

Palo alto college is planning to construct a rectangular parking lot on land bordered on one side by a highway. the plan is to use 720 feet of fencing to fence off the other three sides. what dimensions should the lot have if the enclosed area is to be a maximum?

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  1. 28 January, 20:29
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    The length of the 3 sides has a total dimension of 720 ft. One dimension, the length l, only has one side enclosed. The other dimension, the width w, has 2 sides enclosed. So,

    720 ft = l + 2w

    Rearranging in terms of l:

    l = 720 - 2w

    Then the area equals length times width, or:

    A = (720-2w) (w) = 720w - 2w^2

    To get the maximum area, we take the derivative of the Area equation and set the derivative equal to 0: dA/dw = 0

    dA/dw = 720 - 4w = 0

    720 - 4w = 0

    4w = 720

    w = 180 ft

    Calculating for l:

    l = 720 - 2w

    l = 720 - 2 (180)

    l = 360 ft

    Therefore to get the maximum enclosed area, the width (2 sides) should be 180 ft while the length (1 side) is 360 ft.
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