Problem 4. [30'] A school needs to select 4 players to attend a Badminton Doubles Event. The rank of the average grades in practice sessions and class of each player are as shown below. 2 3 Player 1 Class A A A Rank 5 3 9 Page 2 Player Class Rank 1 A 5 Weight (Lb) 149.87 4 B There are some requirements that need to be satisfied. 30 10 2 A 3 162.35 . Select at least one player from each class; If player 2 is selected, then player 6 must be selected; and if player 6 is selected, then player 2 must be selected; . Either player 3 or 8 must be selected; N (1) [10] The school's goal of the selection is to minimize the average rank. Formulate this problem as an IP model. Clearly define the decision variables, the objective function, and the constraints. 5 6 7 8 9 10 C B B C C 4 1 8 7 2 6 (2) [10] Solve the above IP model by Excel Solver and explain the optimal solution. (3) [10] There is a new regulation concerning the weight gap, that is, the gap between the maximal and average weights of the selected player cannot exceed 5 Lb. The updated information with the weights of players is, 3 4 5 6 7 8 9 A B B B C C C 9 10 4 1 8 7 2 155.31 157.54 155.58 159.17 164.39 155.08 137.22 10 C 6 152.93 Reformulate the IP problem and solve it by Excel solver. Hint: to satisfy the limit on the gap between the maximal weight and the average weight, it is necessary to limit the gap between the weight of all selected players and the average weight.

Problem 4. [30] A school needs to select 4 players to attend a Badminton Doubles Event. The rank of the average grades in practice sessions and class of each player are as shown below. Page 2 There are some requirements that need to be satisfied. - Select at least one player from each class; - If player 2 is selected, then player 6 must be selected; and if player 6 is selected, then player 2 must be selected; - Either player 3 or 8 must be selected; (1) [10] The school's goal of the selection is to minimize the average rank. Formulate this problem as an IP model. Clearly define the decision variables, the objective function, and the constraints. (2) [10] Solve the above IP model by Excel Solver and explain the optimal solution. (3) [10] There is a new regulation concerning the weight gap, that is, the gap between the maximal and average weights of the selected player cannot exceed 5Lb. The updated information with the weights of players is, Reformulate the IP problem and solve it by Excel solver. Hint: to satisfy the limit on the gap between the maximal weight and the average weight, it is necessary to limit the gap between the weight of all selected players and the average weight