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. )