Exercise 15 (ALLOCATION OF FUNDS). If x thousands of dollars are spent on labor and y thousands of dollars are spent on equipment, the output of a certain factory will be Q (x, y) = 60x1 / 3y2 / 3 units. If $ 120,000 is available, how much should be allocated to labor and how much to equipment to generate the maximum possible output?

Exercise 16 (MARGINAL ANALYSIS). Use the Lagrange multiplier, , to estimate the change that will occur in the maximum output of the factory in Problem 24 if the money available for labor and equipment increases by $ 1000.