After the bad start to the season and unexpected injuries, the Dallas Cowboys wants to sign 3 new players. There are five players under consideration. Player 1, 2 and 4 can play the quarterback position and Cowboys want to bring in at least one new player for this position. Each player has a strength given by sj, and Cowboys want to add at least S units of strength to the team by hiring some of these 5 players. On the other hand, the Cowboys will be careful while signing people who are prone to be penalties. Player j is likely to have at. penalties per season and Cowboys impose a quota of A penalties per season for these players. (a) If player j demands the salary cj, make up an IP to decide on which players should be signed to minimize the signing budget. (Just write out the IP) (b) If players 1 and 2 are buddies and will come to Dallas only together, add a constraint to guarantee that either they are signed together or they are not signed at all. (Just write this new constraint) (c) If player 1 hates player 3 and will not come if player 3 comes, add an appropriate constraint that does not allow signing player 1 and 3 together. (Just write this constraint)