<PRE><B>Question 1057214</B>
A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area. 
-------
Perimeter P = w + w*pi/2 + 2h = 500
w*(pi/2 + 1) + 2h = 500
h = 250 - w*(pi/4 + 1/2)
----
Area = w*h + pi*(w/2)^2/2
Sub for h
Area = w*(250 - w*(pi/4 + 1/2)) + pi*w^2/8
Area = (pi/8)*w^2 -w^2*(pi/4 + 1/2) + 250w
Area = (-pi/8 - 1/2)*w^2 + 250w
dArea/dw = (-pi/4 - 1)w + 250 = 0
w = 250/(pi/4 + 1)
w =~ 140.025
h =~ 70.012</PRE>