2. (30 points) Husky has the following preferences over coffee (x) and tea (y) u(r, y) = min(3r, 2y) (a) (6 points) Are Husky's preferences, rational (complete and transitive) and con- tinuous? Explain/prove your answer and state the definitions for completeness, transitivity, and continuity. (b) (5 points) Are Husky's preferences monotone? If yes, are they strongly monotone or weakly monotone? Define weak and strong monotonicity and then prove your answer.(c) (3 points) Are Husky's preferences strictly convex? Prove your answer. (d) (10 points) Graph Husky's indifference curves that go through points (2, 3), (4, 6), (6,9), (8, 12). Be sure to label the axis and the utility levels of the indifference curves. (Hint: You should be graphing 4 indifference curves.)(e) (4 points) On the same graph above, draw a budget constraint where p. = 2, py = 2, and m = 20. Note that careful attention to precise graphing here will help in part (f). Draw on the graph above (f) (2 points) Subject to the budget constraint you drew above, graphically solve for the utility maximization bundle (r*, y*) for this consumer. (Although we haven't discussed the utility maximization special cases, Leontief and Linear, in lecture 3 yet, you should still be able to identify the optimal bundle graphically.)