Optimization

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 45 feet?

so the perimeter is:
pi*r + 2r + 2h = 45.

h= (45 - PIr - 2r)/2

The area equals = (pi*r^2)/2 + 2rh

what do i do from here?

<<what do i do from here?>>
(1) Substitute your h(r) equation into the A (r,h) equation to express Area (A) in terms of r only.
(2) Then compute dA/dr and set it equal to zero.
(3) The solution will be the maximum-area value of r.

(4) Then substitute that r into the A(r) equation to get the maximum area.

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asked by Tom

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