Subject called operations research

Problem 1 Coach Night is trying to choose the starting line-up for the basketball team. The team consists of seven players who have been rated (on a scale of I 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 1. The five-player starting line-up 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 I member must be able to play center. 2. The average ball-handling, shooting, and rebounding level of the starting line-up 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 1 3 Player Position Ball-handling Shooting ReboundingDefense 3 1 3 2 2 3 2 3 G-F 2 3 2 2 4 F-C 1 3 3 5 G-F 3 2 6 F-C 3 2 3 7 G-F 3 2 2