# On the right track with this optimization problem?

• Sep 7th 2012, 04:15 PM
On the right track with this optimization problem?
Question:
A piece of 2 m long wire is to be cut into two pieces one of which is to be formed into a circle and the other into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) the minimum and (b) a maximum?

Pasting in an image appears to be the quickest way to get this posted since I'd have to post an image anyway with my diagrams.
Attachment 24727
I'm concerned that I've gone wrong somewhere because the algebra required to isolate x is beyond me. Usually these things are easier than that. Although my algebra is weak so it wouldn't surprise me if I was missing something simple.
• Sep 7th 2012, 05:08 PM
MaxJasper
Re: On the right track with this optimization problem?
Quote:

Min area :Triangle side $a\to \frac{6}{9+\sqrt{3} \pi }$ & circle dia $d\to \frac{2-\frac{18}{9+\sqrt{3} \pi }}{\pi }$ Min(area)= $\frac{9 \sqrt{3}}{\left(9+\sqrt{3} \pi \right)^2}+\frac{\left(2-\frac{18}{9+\sqrt{3} \pi }\right)^2}{4 \pi }$
Max area is when only we have a circle d= $2/\pi$ Max(area)= $\frac{1}{\pi }$