Hi I am new here and have a calculus question that came up at work.
Suppose you have a 4' x 8' piece of plywood. You need 3 circular pieces all equal diameter. What is the maximum size of circles you can cut from this piece of material? I would have expected I could write a function for the area of the 3 circles in terms of x and y, then differentiate it, find a maxima/minima point and go from there.
My coworker did cut 3 33" circles and that solved the real-world problem. But my passion would be to find the mathematical answer to this. I hope that my new stackexchange.com friends have the same passion, and can help me find the answer to this in general terms.
What I mean by that is someone says I have a piece of material Q units by 2Q units, what are the three circles of maximum size?... I hope you understand what I am asking. I am looking to be a friend and contributor BD