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 the plays abilities are listed below:

The five-player staring lineup must satisfy the following restrictions:

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

The average ball-handling, shooting, and rebounding level of the staring lineup must be at least 2

If player 3 starts, then player 6 cannot start

If player 1 starts, then players 4 and 5 must both start

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.

Player Position Ball-handling Shooting Rebounding Defense 3 3 3 G,F F,C G,F F,C G,F 3 3 3 3 Player Position Ball-handling Shooting Rebounding Defense 3 3 3 G,F F,C G,F F,C G,F 3 3 3 3