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applied math
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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 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. TABLE 9: $$ \begin{matrix} \text{Player} & \text{Position} & \text{Ball-Handling} & \text{Shooting} & \text{Rebounding} & \text{Defense}\\ \text{1} & \text{G} & \text{3} & \text{3} & \text{1} & \text{3}\\ \text{2} & \text{C} & \text{2} & \text{1} & \text{3} & \text{2}\\ \text{3} & \text{G-F} & \text{2} & \text{3} & \text{2} & \text{2}\\ \text{4} & \text{F-C} & \text{1} & \text{3} & \text{3} & \text{1}\\ \text{5} & \text{G-F} & \text{3} & \text{3} & \text{3} & \text{3}\\ \text{6} & \text{F-C} & \text{3} & \text{1} & \text{2} & \text{3}\\ \text{7} & \text{G-F} & \text{3} & \text{2} & \text{2} & \text{1}\\ \end{matrix} $$
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