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Lorenzo lives on x and y alone. His utility function is . The prices of both goods are positive. Which of the following statements is necessarily true?
Georgina consumes only grapefruits and pineapples. Her utility function is ; where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina's income is 105, and the prices of grapefruits and pineapples are 1 and 3, respectively. How many grapefruits will she consume?
Ambrose's brother Bartholomew has a utility function ; where x1 is his consumption of nuts and x2 is his consumption of berries. His income is 115, the price of nuts is 5 and the price of berries is 1. How many units of berries will Bartholomew demand?
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