A football directortriesto form a five playersoccer team. There are seven players who have been graded (on a scale of 1: weak to 3:

A football directortriesto form a five playersoccer team. There are seven players who have been graded (on a scale of 1: weak to 3: perfect)according to their ability 1, ability 2, ability 3, and ability 4. The positions that each player is permitted to play and the abilities of each player are shown in the below table. The formed five player team must satisfy the following constraints: Player Position Ability 1 Ability 2 Ability 3 Ability 4 1 1 3 3 1 3 2 3 2 1 3 2 3 1-2 2 3 2 2 4 2-3 1 3 3 1 5 1-2 3 3 3 3 6 2-3 3 1 2 3 7 1-2 3 2 2 1  At least 4 playersmust be able to play at position 1, at least 2 playersmust be able to play at position 2, and at least 1 player must be able to play at position 3.  The average ability 1, ability 2, and ability 3 of the team must be at least 2.  If player 3 starts, then player 4 cannot start.  If player 1 starts, then players 6 and 5 must both start.  Either player 2 or player 3 must start. Given these constraints, the directorwants to maximize the total ability 4of the team. Formulate an IP fo