Consider a consumer with preferences represented by a utility function u(TI, 12) = 11 + 412. The prices of x1 and x2 are denoted as p, and p2 and income is denoted as m. a) (2 marks) Illustrate the indifference curves of this preference relation. b) (2 marks) Write down the consumer's utility maximisation problem. c) (4 marks) Given prices p=(p1,p2)>0 and income m>0, derive the consumer's demand functions. Explain your steps. d) (1 mark) Does this consumer have homothetic preferences? Provide an explanation. e) (1 mark) Does the Law of Demand hold for x2? Provide an explanation