5. [This question demonstrates how blindly using calculus can lead us astray] Suppose the consumer's utility is given by u(:r) = If + (l + 12):, and their income and prices are given by (UI.P1.P2) = (10.2.3) . In what follows, you may take it for granted that the consumer has some optimal solution to the consumer's problem. (a) Given :1..- E X . write a formula for the marginal utilities MU1(:r) and MIMI). (b) Show that they will optimally spend all their money. (c) A unique bundle 1 exists such that the consumer spends all their money (p - x = m) and their per-price marginal utility is the same for the two goods (2111 = #351). What is it? ((1) What is the consumer's optimal bundle from her budget set