Operations Research: Integer Programming - Modeling

Coach Night is trying to choose the starting lineup for the basketball team. The team consists of seven players who have been rated (on a scale of 1= poor to 3= excellent) according to their ball-handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to play and the player's abilities are listed in the table. The five-player starting lineup must satisfy the following restrictions: 1. At least 4 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 2. The average ball-handling, shooting, and rebounding level of the starting lineup must be at least 2. 3. If player 3 starts, then player 6 cannot start. 4. If player 1 starts, then players 4 and 5 must both start. 5. Either player 2 or player 3 must start. Given these constraints, Coach Night wants to maximize the total defensive ability of the starting team. Formulate an IP that will help him choose his starting team