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A front window on a new home is designed as a rectangle with a semicircle on the top. If the window is designed to let in a maximum amount of light, and the architect fixes the perimeter of the entire window at 600 inches, determine the radius r and rectangular height h so as to maximize the area

  • calculus - ,

    area= w*h+1/2 PI (w/2)^2

    but 600= w+2h+PI*(w/2)

    or h=300-w/2 (PI-1/2)

    area= w(above h) + 1/8 PI w^2
    take the derivative of area wrespect to w

    darea/dw=0=you do it.

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