1. Suppose that a person consumes apples (A) and bananas (B), and has utility function u(A, B) = A1/2 + B1/3. The price of apples is 3, the price of bananas is 4, and income is 24. Use the Lagrange multiplier method to find her optimal bundle. 2. Suppose a person consumes artichokes (A) and bicycles (B), and her utility function is u(A, B) = A + Bb. The prices PA and PB and income m are left general. Use Lagrange multipliers to find her optimal bundle. Hint: you may wish to use an order-preserving transformation before you start the Lagrange multiplier process. What fraction of her income does the person spend on A? What can you conclude about how that that fraction depends on P. P