Suppose that Pete is currently consuming at a level in which his marginal utility of consuming an extra pizza (X) is 10 and his marginal utility of consuming an extra beer (Y) is 2. Assume that his preferences are convex.
a. What is Pete's MRS of pizza for beer? That is, what is the number of beers that he is willing to give up to get one more pizza?
b. Suppose that the price of a pizza is $8.50, and the price of a beer is $2.50. Is Pete maximizing his utility at his current consumption? If not, how should he change his bundle to reach his optimum? Explain your answer using the marginal utility condition at the optimal choice.