State University is scheduling 24 sections of a large computer skills course in the Fall semester. There are eight time slots for these sections, four on Monday/ Wednesday (MW) and four on Tuesday/Thursday (TR). In each time slot, three sections are scheduled. These are shown in the file P06_86.xlsx. The sections will be taught by six instructors. Instructors 1 to 3 must teach at least three sections and no more than four sections each. Instructors 4 to 6 must teach at least four sections and no more than five sections each. The instructors have submitted their top four preferences for time slots, as shown in the file. Four points are awarded for satisfying an instructor’s first preference, three for second preference, two for third preference, and one for fourth preference. These points appear in the file. For example, instructor 1’s preferences are, in decreasing order, MW 9-10, MW 11-noon, MW 1-2, and TR 11-noon. Find an assignment of instructors to sections that maximizes the points from satisfying preferences. Of course, no instructor can teach more than one section in the same time slot.
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