Joana is an 18-year-old girl who is facing some important decisions now that she wants to apply to a business school. The two undergraduate programs she is interested in are Business Administration, which requires the Maths exam, and Marketing and Strategy, which requires only the Economics exam. She is deciding how much effort to put in each of these exams. Suppose that both programs require the same minimum grade and, therefore, she will use the exam where she has the highest grade. Her preferences can be described as u(x, y) = max{x, y}, where x denotes her Maths exam grade and y denotes her Economics exam grade. Notice that her utility depends only on the highest grade she gets. Joana has a total of 44 hours to study for both exams. She estimates that to get an extra point in the Maths exam (x), she needs to study 4 hours, while for an extra point in the Economics exam (y) she needs to study 2.5 hours. Therefore, her time-constraint can be described by 4x + 2.5y = 44. What is the maximum grade she can get in the Maths exam? What about the Economics exam?
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