Posted by Cvan on .
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 
bobpursley,
area= w*h+1/2 PI (w/2)^2
but 600= w+2h+PI*(w/2)
or h=300w/2 (PI1/2)
area= w(above h) + 1/8 PI w^2
take the derivative of area wrespect to w
darea/dw=0=you do it.