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14 December, 19:04

Due to an influx of wild animals, you need to enclose your garden. You have 500 feet of fencing and will enclose the garden on three sides, with your barn providing protection for the fourth size. Determine the length of the fence opposite the barn which maximizes the area enclosed.

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  1. 14 December, 19:14
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    so length of the fence is 250 feet

    Explanation:

    Given data

    fencing (L) = 500 feet

    enclose the garden = 3 sides

    to find out

    length of the fence

    solution

    we consider barn length x and width y

    so we say x + 2y = 500 ... 1

    we want to maximize length i. e xy = f

    so we say

    df/dx = ƛ * dL/dx

    y = ƛ * 1

    and

    df/dy = ƛ * df/dy

    x = ƛ * 2

    from equation 1 we can say

    2 ƛ + 2 ƛ = 500

    so ƛ = 500/4 = 125

    so that x = 2 * 125, y = 125

    so x = 250, y = 125

    so length of the fence is 250 feet
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