Thread: Maximization Problem Help

Here's my question...

A Norman window, one that is formed by placing a semicircle on top of a rectangle, still remains a popular architectural feature. If the perimeter of the window is 300cm, find the radius of the semicircle that will maximize the window's area (let in the most light).

I came up with this equation... 300 = 2x + y + ((pi*y)/2)
x = rectangle height
y = rectangle width

These questions really bug me and I'm really stuck! Help please!

Originally Posted by lionpants

Here's my question...

A Norman window, one that is formed by placing a semicircle on top of a rectangle, still remains a popular architectural feature. If the perimeter of the window is 300cm, find the radius of the semicircle that will maximize the window's area (let in the most light).

I came up with this equation... 300 = 2x + y + ((pi*y)/2)
x = rectangle height
y = rectangle width

These questions really bug me and I'm really stuck! Help please!

First I'd let the width of the rectangle be 2y so that the radius of the semi-circle is y.

Then 2x + 2y + pi y = 300 and you can re-arrange this to make x the subject.

A = 2xy + pi y^2 and you can sub x in terms of y from the above.

So you have A as a function of y.

Now solve dA/dy = 0 for y and test that this corresponds to a maximum.