(50pts) Michael Malone is trying to choose a starting lineup for a basketball team that will compete in the summer league. The team consists of seven players who have been rated (on a scale of 1 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 below.
The five-player starting lineup must satisfy the following restrictions:
1) At least 2 members must be able to play guard, at least 2 members must be able to play forward, and at most 1 member must be able to play center.
2) The average shooting level of the starting lineup must be at least 2, while the average defense level of the guards in the lineup must be at least 2.5.
3) If player 6 does not start, then player 4 has to start.
4) Either player 1 or player 5 must start.
5) If player 7 starts, then player 5 must also start and player 3 cannot start.
Given these constraints, Coach Boyle wants to maximize the total shooting ability of the starting team. Formulate an Integer Program that will help him choose his starting team. Clearly define the decision variables, objective function, and constraints.
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