Rajit is an editor who has been allotted $60,000 to spend on the development and promotion of a new book. He estimates that if x thousand dollars are spent on development and y thousand dollars on promotion, approximately S(x, y) = 20x^3/2y copies of the book will be sold.

a. How much money should Rajit allocate to development and how much to promotion to maximize sales? What is the maximum sales level?

b. If Rajit is allotted an extra $1,000 for development and promotion, how much should he expect the maximum sales level to change? Base your answer on the Lagrange multiplier λ.