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The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area.

  • Calculus -

    If the printed area has width x and height y,
    xy = 386

    The total area is thus
    a = (x+8)(y+4) = (x+8)(386/x + 4)
    = 4x + 418 + 3088/x

    max area is where da/dx=0

    da/dx = 4 - 3088/x^2
    so, da/dx = 0 when x = 2√193

    Now just evaluate y.

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