Problem 2: Lucy is a utility maximizing consumer who has the following utility function for takeout meals (T) and food at home (F). U = 3T /3F /3 A. Given Lucy's utility function: (3 pts) i. What is Lucy's marginal utility of takeout, T? ii. Is more takeout better? iii. What happens to her marginal utility as consumption of takeout becomes large? Assume Lucy's monthly budget for all meals (takeout and food at home) is $270. The price of takeout is $15 and food at home is $5. B. Write out Lucy's budget constraint. (2 pts) C. What is Lucy's optimal consumption bundle of T and F? (4 pts) D. Graph Lucy's utility maximization problem. Indicate the point where her optimal consumption of T and F is on your graph. Remember to label everything. (3 pts)