The head of the Department of Business Analytics at Tech is determining faculty teaching schedules for the department’s 10 faculty members for next semester. There are 20 course sections scheduled over six 75-minute class periods on Tuesdays and Thursdays with 15 minutes in between classes—8T, 9T, 11T, 12T, 14T, and 15T—where 8T is at 8 a.m., 9T is at 9:30 a.m., 11T is at 11 a.m., 12T is at 12:30 p.m., 14T is at 2 p.m., and 15T is at 3:30 p.m. Each faculty member will be assigned two courses to teach. At the beginning of the academic year the head asks each faculty member to rank their course teaching preferences from 1 to 5, with 1 being “very desirable,” 3 being “indifferent,” and 5 being the “least desirable.” The following table shows the course class periods and the faculty members’ preferences for each course:

a. Formulate and solve a linear programming model to determine a teaching schedule that will satisfy the faculty members’ teaching preferences as closely as possible.
b. Professors Abrahams, Brinton, and Holt have young children, and thus they prefer not to have classes at 8T, so they can get their kids off to school in the morning, and at 15T, so they will be home when their kids get home from school in the afternoon. Determine a teaching schedule that reflects these additional preferences.

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Faculty 3424, 3434, Member 9T, 11T 8T, 14T Abrahams 3 4 4 3 5 2 3 3 4 Brinton Clark Deane Everett Fogel Grady Holt Iman Jared 4 4 3 3 4 1 3 1 1 3 3444, 8T, 12T 1 2 2 2 4 1 3 3 3 1 3454, 9T 3 1 1 5 4 Course 5 5 5 4 5 4434, 8T, 11T, 12T 2 4 3 3 5 4 3 5 3 5 4444, 8T, 9T, 15T 5 5 4 4 3 3 4 4 5 3 4454, 11T, 14T, 15T 5 5 4 2 3 3 2 5 5 3 4464, 8T, 9T 5 4 4 5 5 4 4 3 5 4