Suppose that U = min{2X, 0.5Y}, where X is units of good X and Y is units of good Y. The price of good X is $1 and the price of good Y is $2. What is the minimum expenditure necessary to achieve a utility level of 100?

The consumer's budget constraint is $6 = 0.50G + P, where G is packs of gum and P is bags of pretzels. If the consumer's utility function is U = G^0.5*P, what is the utility-maximizing bundle of gum and pretzels? (Note: The marginal utility of pretzels MUP = G^0.5 and the marginal utility of gum MUG = 0.5G^-0.5*P.)

Nancy's ratio of marginal utilities for coffee and lipstick is 3/1, while the price ratio of coffee to lipstick is 1.5/1. Which of the following statements is TRUE?
I. Coffee provides Nancy with 3 times the utility of lipstick.
II. Nancy could increase utility by decreasing her consumption of coffee by 3 units and increasing her consumption of lipstick by 1.5 units.
III. Nancy could increase utility by decreasing her consumption of lipstick by 3 units and increasing her consumption of coffee by 2 units.
IV. Nancy could increase utility by decreasing her consumption of coffee by 1 unit and increasing her consumption of lipstick by 3 units.