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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    A rectangular garden is to be surrounded by a fence joined to a 3 m long wall on one side. The opposite side to the wall has a 1 m opening ( for a later gate). There is40 m of fencing available. To maximize the garden area, the length of fence to be added to the wall side is:

    Thank you.
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  2. #2
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    Quote Originally Posted by Hakhengkim View Post
    A rectangular garden is to be surrounded by a fence joined to a 3 m long wall on one side. The opposite side to the wall has a 1 m opening ( for a later gate). There is40 m of fencing available. To maximize the garden area, the length of fence to be added to the wall side is:

    Thank you.
    let L = total length of the side with the wall

    W = length of the side perpendicular to L

    40 = (L - 3) + (L - 1) + 2W

    22 = L + W

    W = 22 - L

    area, A = LW = L(22 - L)

    shouldn't need calculus to find the value of L that maximizes the area.

    remember that the question is asking for the value of (L - 3).
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