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The owner of a used tire store wants to construct a fence to enclose a rectangular outdoor storage area adjacent to the store, using part of the side of the store (which is 220 feet long) for part of one of the sides. (See the figure below.) There are 430 feet of fencing available to complete the job. Find the length of the sides parallel to the store and perpendicular that will maximize the total area of the outdoor enclosure.
Length of parallel side(s)=?
Length of perpendicular sides=?

  • Calculus -

    let the side parallel to the store by y
    let the two other sides be x
    y + 2x = 430
    y = 430 - 2x

    area = xy
    = x(430 - 2x)
    = 430x - 2x^2
    d(area)/dx = 430 - 4x = 0 for a max area
    4x = 430
    x = 107.5

    I will let you finish it.

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