
Optimization problem
This problem is giving me some trouble. It's irritating because it seems so easy.
The question is
"The figures are made of rectangles and semicircles.
a.) Find a formula for the area
b.) Find a formula for the perimeter
c.) Find the dimensions x and y that maximize the area given that the perimeter is 100"
The figure is a rectangle with sides x and y with a halfcircle connected to one of the ends (diameter of the circle is equal to y).
I got A=xy + 1/2*(1/2y)^2 for the area and
P=2x + y + (1/2)(y)(pi) for the perimeter.
The book gives the answer for c.) as x=100/(4+pi) and y=200/(4+pi)
No matter what I try I can't seem to get their answer. I know I have find the value of x (or y) in terms of the other variable using 100 but I keep getting y=63.661977 and x=31.83098869. I'm stumped.

Re: Optimization problem
The area of a (full) circle is (with being circle radius). I think there's a factor missing in your formula for the area.

Re: Optimization problem