Ulem University uses a mathematical model that optimizes student preferences taking into account the limitation of classroom and faculty resources. To demonstrate the application of the model, consider the simplified case of 10 students who are required to select two courses out of six offered electives. The table below gives scores that represent each student's preference for individual courses, with a score of 100 being the highest. For simplicity, it is assumed that the preference score for a two-course selection is the sum of the individual score. Course capacity is the maximum number of students allowed to take the class.

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Preference score for course Student 20 40 50 30 90 100 90 100 80 70 0 40 25 80 75 60 90 100 50 60 40 90 10 80 80 45 40 70 60 55 30 100 40 70 90 55 80 40 40 30 80 95 90 40 40 4 60 60 100 7065 60 80 100 90 80 10 10 Course capacity 6