Suppose that a person has strongly convex preferences. Suppose that the budget line 10 = 2X + y for the goods X and y. Argue that no matter what the utility function looks like, it cannot be true that both (4,2) and (2,6) are optimal even though both are on the budget line. Hint: Use a diagram with standard indifference curves. Now, suppose that the preferences are u(X, y) = 2X + y, which are not strongly convex. Using the same budget line, argue that both (4,2) and (2,6) are optimal.