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 Fall Preference 3. 5. Spring Preference 4 3 4 Marketing 4 5 Finance 6 4 Production 4 6 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 P P2, P3 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. (Continuing from Problem 1) What will the cost in the network be if Professor 1 were to teach a Production course at Spring Semester? (Continuing from Problem 1) What do you account for the fact that at least one class has to be offered each Semester? O Set rij of the edge from node (Professor) to node (Class, Semester) to be greater than 1 O Set aij of the edge from node (Class, Semester) to node (Class) as 1 O Set uij of the edge from node (Class, Semester) to node (Class) as 3 O Set uij of the edge from node (Class, Semester) to node (Class) as -3 (Continuing from Problem 1) What is the sum of b; (net supply) of the source node s and sink nodes t? O 6 O 12 O 24 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 Fall Preference 3. 5. Spring Preference 4 3 4 Marketing 4 5 Finance 6 4 Production 4 6 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 P P2, P3 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. (Continuing from Problem 1) What will the cost in the network be if Professor 1 were to teach a Production course at Spring Semester? (Continuing from Problem 1) What do you account for the fact that at least one class has to be offered each Semester? O Set rij of the edge from node (Professor) to node (Class, Semester) to be greater than 1 O Set aij of the edge from node (Class, Semester) to node (Class) as 1 O Set uij of the edge from node (Class, Semester) to node (Class) as 3 O Set uij of the edge from node (Class, Semester) to node (Class) as -3 (Continuing from Problem 1) What is the sum of b; (net supply) of the source node s and sink nodes t? O 6 O 12 O 24 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 Fall Preference 3. 5. Spring Preference 4 3 4 Marketing 4 5 Finance 6 4 Production 4 6 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 P P2, P3 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. (Continuing from Problem 1) What will the cost in the network be if Professor 1 were to teach a Production course at Spring Semester? (Continuing from Problem 1) What do you account for the fact that at least one class has to be offered each Semester? O Set rij of the edge from node (Professor) to node (Class, Semester) to be greater than 1 O Set aij of the edge from node (Class, Semester) to node (Class) as 1 O Set uij of the edge from node (Class, Semester) to node (Class) as 3 O Set uij of the edge from node (Class, Semester) to node (Class) as -3 (Continuing from Problem 1) What is the sum of b; (net supply) of the source node s and sink nodes t? O 6 O 12 O 24