Optimization

[mrcherv]

Attaching my work so far, don't think i'm doing it right but maybe i am..if not could someone tell me where i'm going wrong?
"4 feet of wire will be used to make a circle & a square...how much wire should be used in the circumference of the circle to maximize the area enclosed by both shapes?"
Thank you!

 

[srmichael]

I would like to help, but I can't read the attachments. What I can provide is the general method for doing a problem like this. You want to maximize the area of the sum of both the circle and the square. So you know can come up with this formula with "r" as the radius of the circle and "s" as the length of one of the sides in the square. But now you have two variables in this equation so you must use another equation to solve for one variable in terms of another and then substitute into the area formula. You were told the total length of the the wire is 4 feet so the sum of the circumference of the circle and the perimeter of the square must equal 4. From this equation you can solve for one variable in terms of another, plug into the area formula and then proceed from there.....