2. The professor in charge of a management science class is faced with the problem of assigning 14 students to four projects (P1, P2, P3 and P4) in four different partner companies. Each student must be assigned to only one project, and each project group must have 3 or 4 students. The students have been asked to rank the projects, with 1 being the best ranking and 6 representing the lowest preference. Their rankings are presented below. P1 P2 P3 P4 P1 P2 P3 P4 Ann 1 3 4 6 Hadi 74 1 2 Ianna 4 6 2 1 Ben 64 2 5 Cora 6 2 3 1 Jake 6 54 Dean 5 51 2 Kay 5 2 31 Ella 6 5 1 3 Leo 46 31 Finn 4 6 21 Mia 4 2 1 5 Nasir 5 6 4 2 Gia 5 6 4 2 O Cristina del Campo 1/2 a) Formulate an assignment model so the students as a group are given their most preferred option as possible. State all the elements and label all constraints b) Solve the assignment problem in part a and interpret the solution. c) How many students are assigned their second or third choice? 2. The professor in charge of a management science class is faced with the problem of assigning 14 students to four projects (P1, P2, P3 and P4) in four different partner companies. Each student must be assigned to only one project, and each project group must have 3 or 4 students. The students have been asked to rank the projects, with 1 being the best ranking and 6 representing the lowest preference. Their rankings are presented below. P1 P2 P3 P4 P1 P2 P3 P4 Ann 1 3 4 6 Hadi 74 1 2 Ianna 4 6 2 1 Ben 64 2 5 Cora 6 2 3 1 Jake 6 54 Dean 5 51 2 Kay 5 2 31 Ella 6 5 1 3 Leo 46 31 Finn 4 6 21 Mia 4 2 1 5 Nasir 5 6 4 2 Gia 5 6 4 2 O Cristina del Campo 1/2 a) Formulate an assignment model so the students as a group are given their most preferred option as possible. State all the elements and label all constraints b) Solve the assignment problem in part a and interpret the solution. c) How many students are assigned their second or third choice