. Suppose that a person has strongly convex preferences. Suppose that the budget line 10 = 2 + for the goods and . 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 (, ) = 2 + , which are not strongly convex. Using the same budget line, argue that both (4,2) and (2,6) are optimal.