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Alvaro's preferences can be represented by the utility function u(1 1 , 12) = (17 +24 ). Bella's preferences can be represented by the utility function u(1, 12) = (21+12)2. (a) Consider first Alvaro. Sketch a graph* containing his indifference curve through the point (4, 4) as well as the indifference curve for the utility level of 4. (b) Are Alvaro's preferences monotonic? Explain your answer. (c) Are Alvaro's preferences convex? Explain your answer (d) Write down Alvaro's utility maximisation problem and find Alvaro's demand functions TI(P1, P2, m) and x2(P1, P2, m). (e) Now consider Bella. Sketch the indifference curve through the point (0, 4) as well as the indifference curve for the utility level of 25. (f) Are Bella's preferences monotonic? Are they convex? (g) How much does Bella demand of the two goods if her income is m = 20 and prices are P1 = 1 and p2 = 2