What is an appropriate objective function for this scenario?

The department chair reviewed last year's schedule, the degree requirements for the ever popular Operations and Supply Chain major, and the emails that had drifted into her mailbox over the last week. Naturally, every professor in the department had his own pet course and wanted to maintain control of it while avoiding 8 a.m. classes at all costs. In an effort to placate the senior faculty members of the department, the chair sent an email asking them to supply the prep time for each of the classes they were qualified to teach, promising to assign them the least taxing schedule possible. Each of her department members had to teach at least two courses, but no more than three. The elective courses, Project Management, Quality Management, Control and Planning, Logistics, and Management Science each had to be offered once and the department needed to offer at least six sections of the Introduction to Operations class. The prep times each professor estimated for each course appear in the table below.

Intro to Ops Project Mgt Quality Mgt Control Logistics Mgt Science
Saba 3 10 12 16 12 7
Geoff 4 19 2 10 8 18
Tim 5 11 4 14 14 3
David 4 11 4 15 17 15

A) Max Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM +
5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM
B) Min Z = 3SI + 10SP + 12SQ + 16SC + 12SL + 7SM + 4GI + 19GP + 2GQ + 10GC + 8GL + 18GM +
5TI + 11TP + 4TQ + 14TC + 14TL + 3TM + 4DI + 11DP + 4DQ + 15DC + 17DL + 15DM
C) Min Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM +
TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM
D) Max Z = SI + SP + SQ + SC + SL + SM + GI + GP + GQ + GC + GL + GM +
TI + TP + TQ + TC + TL + TM + DI + DP + DQ + DC + DL + DM

Answer: B