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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 Table 9. 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 rebound- ing 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. TABLE 9 Ball- Handling Player Position Shooting Rebounding Defense 3 1 3 1 3 2. 3 2 2 1 2 3 4 5 6 G G-F F-C G-F F-C G-F 3 2 2 1 3 3 3 3 1 3 3 3 3 2 1 2 3 1 7 2