Question $5$:

A university has three professors who each teach four courses per year. Each year, four sections of marketing, finance, and production must be offered. At least one section of each class must be offered during each semester $($fall and spring$).$ Each professor's time preferences and preference for teaching various courses are given below.

The total satisfaction a professor earns teaching a class is the sum of the semester satisfaction and the course satisfaction. Thus, professor $1$ derives a satisfaction of $\backslash (3+3=6\backslash )$ from teaching marketing during the fall semester.

Part A: Formulate the problem as a minimum cost network flow problem that can be used to assign professors to courses to maximize the total satisfaction of the three professors. Draw the network and identify the nodes and arcs.

Part B: Solve the problem $($provide exact values for all variables and the optimal objective function$).$