4. Minnie enjoys dessert by eating chocolate cake (C) and apple pie (P) according to the utility function U = Min [0, P]. In any given week, Minnie spends 20 to purchase these two products. Assume that Minnie is a utility maximiser and has to pay 50p for a unit of apple pie and 2 for a unit of chocolate cake. (i) Consider the bundle C = 20 and P = 5. Is this the utility maximizing choice subject to Minnie's budget? (10 marks) (ii) Suppose that Minnie chooses the exact bundle that maximizes her utility. How would the utility maximizing choice of C be affected if price of P went up? (10 marks) (iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can nd out the optimal consumption bundle for a consumer. (20 marks)