1. You have $100 to spend on food, housing, and clothing. Explain how their marginal utilities should be related to their respective prices to maximize utility. Generalize the result for any number of commodities.
2. Suppose Mary spends $50 per month on pizza and soda. She would like to know if she is purchasing the combination of pizza and soda that results in the highest utility possible from her $50 expenditure. She knows that she got 250 utils from the last slice of pizza she ate, and 25 utils from the last soda she drank. Pizza costs $5 per slice and soda costs $1 per can. Advise Mary on her expenditure patterns for next month.