QUESTION 2: Binary Integer Programming (24 points): A sportswriter has chosen an all-star basketball team, 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 Fouls per Teamwork average game Agnew Center 30.2 4.1 2. Bellinger Guard 12.5 1.3 5 Derry Forward 22.7 2.5 3 Ezell Center 19.6 3.8 4 Fossner Guard 23.9 4.1 5 Hecht Center/Forward 25.7 2.3 5 Ingalls Guard 32.1 3.3 3 Jackson Forward 18.6 2.4 3 Langtry Guard/Forward 25.9 3.1 3 a. Define the decision variables you would use to select the starting five. (3 points) b. If your objective is to select a team that will play well together, write the corresponding objective function to maximize teamwork. (3 points) c. The starting five must consist of one "Center" position, two "Guard position, and two "Forward" position. Five people must be chosen. Write the corresponding constraints. (6 points) d. The starting five should produce a scoring average of at least 25 points per player. Write the corresponding constraint. (3 points) e. Bellinger and Derry are from the same team and should not both be selected. Write the corresponding constraint. (3 points) f. If Hecht is selected, then Ingalls must be selected and vice versa. Write the corresponding constraint. (3 points) g. The total number of fouls from the starting five should not exceed 14. Write the corresponding constraint. (3 points)