3. [6 Marks] Consider a consumer with preferences represented by a utility function u(1, T2) = max {X1, $2}. The prices of 1 and 12 are denoted as pi and p2 and income is denoted as m. (a) (2 marks) Illustrate the indifference curves of this preference relation. (b) (1 mark) Write down the consumer's utility maximisation problem. (c) (3 marks) Given p = (P1, P2) > 0 and income m > 0, derive the consumer's demand functions