Joan is enrolled in four courses (course 1, 2, 3, 4) in the IEOR department. She has 35 hours to study in the week before the midterm and wishes to allocate her time to maximize her mid-term grades in these classes. With no effort, suppose her score is ej on course j. Suppose each hour devoted to course j improves her score by pj. She does not want to spend too much time on courses 1 and 2, as she is already quite good at those, so she limits her time on these collectively to 10 hours. Moreover, she wishes to spend the most time on course 4. How should she allocate her time to maximize her overall mid-term score?