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March 24, 2017

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You are creating a rectangular garden and want to surround it with brick edging. You also are going to divide it into two halves with the edging so that your vegetables and herbs are on one side and flowers are on the other.
You only have 120 ft worth of brick edging and want to enclose the most are possible. Determine the dimensions (Length and Width) that will maximize the total area of the garden, and state that maximum area

  • Calculus - ,

    you will have 2 strips of length x and 3 strips of length y.

    2x+3y = 120
    the area a is
    a = xy = x(40 - 2/3 x) = 40x - 2/3 x^2
    da/dx = 40 - 4/3 x
    for max area, da/dx=0, so x = 30

    Thus y=20, and the edging is evenly divided between width and length.

    max area is thus 600 ft^2

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