QUESTION 2: BIP Formulation (24 points): A basketball team is about to be chosen and now must put together the ideal staffing of five. The players' statistics are shown in the table below. The defense rating and teamwork rating are subjective evaluations from 1 to 5, with 5 being the best. The players who have two positions listed can play at either position. Player Position Scoring Turnovers Fouls per Defense Teamwork average per game game rating Agnew Center/Forward 30.2 4 4.1 4 Bellinger Guard/Center 14.5 0.5 1.3 5 W U w Jackson Forward 22.7 2.1 2.5 2 Ezell Center 19.6 3.6 3.8 4 4 Fossner Guard/Forward 23.9 4.4 4.1 5 5 Hecht Center 25.7 1.8 2.3 5 Ingalls Guard 32.1 4.1 3.3 2 (a) Define the seven binary decision variables you would use to select the team. (3 points) (b) If your objective is to select a team that will play well together, write an objective function to maximize teamwork. (2 points) (c) The team must consist of one center, two guards, and two forwards. Five people must be chosen. Write the corresponding constraints. (6 points) (d) The team should have a total defensive rating of at least 16. Write the corresponding constraint. (2 points) (e) The team should produce a scoring average of at least 23 points per player. Please note that the team is five players/people. Write the corresponding constraint. (2 points) (f) Ezell and Hetch should not both be selected. Write the corresponding constraint. (3 points) (g) If Fossner is selected, then Ingalls must be selected and vice versa. Write the corresponding constraint. (3 points) (h) Must select Agnew if Jackson and Bellinger are selected. Write the corresponding constraint. (3 points)