AP Calculus

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. find the dimensions of a norman window of maximum area if the total perimeter is 72 units. Base value is 21.

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  1. if the rectangle is x wide by y high, then the diameter of the window is x.

    So
    x + 2y + π/2 x = 72
    thus, y = [72-(1 + π/2)x]/2

    The area is
    a = xy + π/8 x^2
    = x[72-(1 + π/2)x]/2 + π/8 x^2
    = 36x - (1+π/4)x^2 + π/8 x^2
    = 36x - (1 + 3π/8)x^2

    da/dx = 36 - (2 + 3π/4)x
    da/dx=0 when
    x = 36/(2+ 3π/4)) = 144/(8+3π)
    now you can easily find y.
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    right?

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