Integer Programming, Operations research , Excel Solver

2. Phil Jackson 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 1=poor to 3=excellent) according to their ball- handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to play (G=guard, C=center, F=forward) and the player's abilities are in the table. player Position Ball-Handling Shooting rebounding Defense C G,F M M F,C G,F FC GF M M - | M 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 one member must be able to play center. 2. The average ball-handling, shooting, and rebounding level of the starting lineup must each 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 wants to maximize the total defensive ability of the starting team. Formulate an IP will help him choose his starting team. [30 points]