
New Member
optimization: maximize area of rectangle inside track
I have this problem i cannot figure out. It uses optimization:
There is a rectangular field with a semicircle on each end and a track around the whole thing. The perimeter of the inner edge of the track is 1256 meters.
I need to maximize the area of the rectangle. How do I do this?

Elite Member
You know the perimeter of the track:
[tex]\L\\1256=2x+2{\pi}r[/tex]...[1]
The area of the rectangle is:
[tex]\L\\2rx[/tex]...[2]
Solve [1] for x, sub into [2], differentiate, set to 0 and solve for r.
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