Problem 1 State 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 duringeach semester (fall and spring). Each professor's semester preference and preference for teaching variouscourses is given in the table below. Professor 1 Professor 2 Professor 3 4 4 Fall Preference Spring Preference Marketing Finance Production 4 4 The total satisfaction a professor earns by teaching a class is the sum ofthe semester satisfaction and the course satisfaction. Thus, professor 1 derives a satisfaction of 3+6 9 fromteaching marketing during the fall semester. Formulate a min cost network flow problem (MCNFP) that canbe used to assign professors to courses so as to maximize the total satisfaction of the three professors. Denote P1 P2.Ps as three professors, and M. F. P as Marketing, Finance Production respectively Formulate the above problem as a Minimum Cost Flow Network Problem (MCFNP) that can be used to minimize the total cost incurred in meeting the demand of courses