Wire of length 12 m is divided into two pieces and each piece is bent into a square. How should this be done in order to minimize the sum of the areas of the two squares?
(a) Express the sum of the areas of the squares in terms of the lengths x and y of the two pieces.
(b) What is the constraint equation relating x and y?
(c) What is the interval of optimization? Is it open or closed?
(d) Solve the optimization problem.