Reference no: EM132862147
1) Coach Boyle 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 below.
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.
Either player 2 or player 3 must start.
Given these constraints, Coach Boyle wants to maximize the total defensive abilityof the starting team. Formulate an Integer Program that will help him choose his starting team. Clearly define the decision variables, objective function, and constraints.