HOMEWORK 1: A wire of length L is cut into two pieces: one to be used to form the perimater of a square, and the other a circle. How should the wire be cut in order that the sum of the areas be as small [and also as large] as possible? Set this up as an optimization problem. What is the objective function and what are the constraints? Do the problem in two different ways: as a one variable problem, and also as a two variable problem using the Lagrange multiplier principle.