anybody good at optimization? i am stuck on an online answer problem and the answer key has a mistake in it

Question

anybody good at optimization?  i am stuck on an online answer problem and the answer key has a mistake in it

anonymous · Answer

post it, you will get lots of answers i am sure

anonymous · Answer

A window is being built and the bottom is a rectangle and the top is a semicircle.  If there is 12 meters of framing materials what must the dimensions of the window be to let in the most light?

anonymous · Answer

to let in the most lite it should have the maximum area
A=lb
we have perimeter= 2b+l+pi*l/2=12
substitute b from above equation in the area equation and maximise area with respect to l
you get length from that find b

anonymous · Answer

b=6-(2+pi)*l/4
A=6l-(2+pi)l^2/4

anonymous · Answer

thank you!