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Integer programming model

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The Decision Sciences department head at a university will be scheduling faculty to teach courses during the coming fall semester. Three required courses need to be scheduled. The three courses are at the UG, MBA, and MS levels. Three professors will be assigned to the courses, with each professor receiving one of the courses. Student evaluations of professors are available from previous terms. Based on a rating scale of 5, the average student evaluations for each professor are shown below.
Course
Professor UG MBA MS
A 3.4 4.2 4.3
B 4.6 3.9 4.0
C 4.3 4.2 -

Professor C does not have a Ph. D. and cannot be assigned to teach the MS-level course. If the department head makes teaching assignments based on maximizing the student evaluation ratings over all three courses, what staffing assignments should be made?

Formulate an integer programming model for this assignment problem by determining
(a) The decision variables.
(b) The objective function.
(c) All the constraints.
Note: Do NOT solve the problem after formulating.

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