Problem 1: Consider the problem of assigning students to seminars to minimize the average assigned ranking for all students. Let us define the following notation: INPUTS and SETS J set of students K set of seminars rjk ranking of seminar kK by student jJ. A ranking of 1 is the student's first choice, a ranking of 2 is her second choice, and so on. sk Capacity of seminar kK. This is the maximum number of students that can be assigned to the seminar. We need to decide which students should be assigned to which seminars. Thus, we have the following decision variable: DECISION VARIABLES Xjk1 if student jJ is assigned to seminar kK;0 if not a) Using this notation, formulate the objective of minimizing the sum of the assigned rankings. Note that this will also minimize the average assigned ranking. b) Using this notation, write down the constraints that say that the maximum number of students that can be assigned to a seminar is sk. c) Write down a constraint that says that each student is assigned to at least two seminars. d) Write down a constraint that says for any given seminar, a student can be assigned to that seminar at most one time. e) Write down the non-negativity constraints. Problem 1: Consider the problem of assigning students to seminars to minimize the average assigned ranking for all students. Let us define the following notation: INPUTS and SETS J set of students K set of seminars rjk ranking of seminar kK by student jJ. A ranking of 1 is the student's first choice, a ranking of 2 is her second choice, and so on. sk Capacity of seminar kK. This is the maximum number of students that can be assigned to the seminar. We need to decide which students should be assigned to which seminars. Thus, we have the following decision variable: DECISION VARIABLES Xjk1 if student jJ is assigned to seminar kK;0 if not a) Using this notation, formulate the objective of minimizing the sum of the assigned rankings. Note that this will also minimize the average assigned ranking. b) Using this notation, write down the constraints that say that the maximum number of students that can be assigned to a seminar is sk. c) Write down a constraint that says that each student is assigned to at least two seminars. d) Write down a constraint that says for any given seminar, a student can be assigned to that seminar at most one time. e) Write down the non-negativity constraints