I need help with solving this Optimization problem?

Posted on 2015-11-26 07:22:00 in Math by BILL

A wire 60 inches long is to cut into two pieces. One of the pieces will be bent into the shape of a circle and the other into the shape of an equilateral triangle. Where should the wire be cut so that the sum of the areas of the circle and triangle is minimized? Maximized?

I tried setting it up but I got stuck. Am I on the right track?

I started with the first piece having the length of x and is bent into the equilateral triangle and the other piece having the length of 60-x bent into a circle.

I know the circumference is 2?r = 60-x, and solving for r would be 60-x/2?. I know the area of the triangle is ?3/4(x^2). So wouldn't the total area of the pieces be ?3/4(x^2) + ?r^2?

If I plugged the values in, I would get A = ?3/4(x^2) + ?(60-x/2?)^2, right? What do I do from there?

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