Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I just needed help starting off this problem:

"A 1-km racetrack is to be built with two straight sides and semicricles at the ends. Find the dimensions of the track that encloses the maximum area."

There was a similar question which I did before this which involved a Norman window. My idea was, in order to make everything in terms of one variable, let's say the width, I made radius equal to half of the width. The problem is that I DO get an answer but my textbook says that the answer is "a circular track with a radius of 1/2pi km". I find that weird because it says "racetrack is to be built with two straight sides...."

Anyways I just wanted to know, how should I set up the perimeter and area equations? I know the perimeter is 1km but should I solve for y by making r = half of y (width) or should i keep two variables and try to work with them? (width & radius)

Thanks!

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# Optimization Problem

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