needs to be solved subjectively

Question 2 (20 points): Coach Ataman is trying to choose the starting lineup for the Turkish National Basketball Team. The team consists of seven players who have been rated (on a scale of l=poor to 3=excellent) according to their attacking and defensive abilities. The positions that each player is allowed to play and the player's abilities are listed in below table. The following restrictions have to be satisfied: 1. The starting lineup must consist of exactly five players. (1 constraint) 2. At least 3 members must be able to play guard, at least 2 members must be able to play forward, and at least 1 member must be able to play center. (3 constraints) 3. The average attacking level of the starting lineup must be at least 2. (1 constraint) 4. If player 3 starts, then player 6 cannot start. (1 constraint) 5. If player 1 starts, then players 4 and 5 must both start. (1 constraint) 6. At least one of player 2 and player 3 must start. (1 constraint) Given these constraints, Coach Ataman wants to maximize the total defensive ability of the starting team. Formulate an integer programming (IP) model that will help him choose his starting team. Clearly state the decision variables, objective function, and constraints. Do not try to solve the problem. Player Position Attacking Defense 1 G 1 3 2 2 2. 2 3 G-F 3 2 4 F-C 3 1 5 G-F 3 3 3 3 6 F-C 1 3 7 G-F 2 2 G: Guard F: Forward C: Center