Consider the following assignment problem:

After reviewing last year's schedule, degree requirements for the Operations and Supply Chain major, and emails received over the past week, the department chair addressed the concerns of the professors in the department. Each professor had their own favored course and desired to avoid early morning classes. To accommodate the senior faculty, the chair requested prep times for the courses they were qualified to teach and assured them of a schedule with minimal stress. All department members must teach at least two courses, with a maximum of three. Additionally, the department must offer each elective course $-$ Project Management, Quality Management, Control and Planning, Logistics, and Management Science $-$ at least once. Six sections of Introduction to Operations class must also be provided. The estimated prep times for each course are listed in the table below.

$$ Intro to Ops $($I$)$ Project Mgt $($P$)$ Quality Mgt $($Q$)$ Control $($C$)$ Logistics $($L$)$ Mgt Science $($M$)$

Saba $($S$)3101216127$

Geoff $($G$)419210818$

Tim $($T$)511414143$

David $($D$)4114151715$

What is an appropriate objective function for this scenario?