During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair

 During the campus Spring Fling, the bumper car amusement attraction has a problem of cars becoming disabled and in need of repair. Repair personnel can be hired at the rate of $20 per hour, but they only work as one team. Thus, if one person is hired, he or she works alone; up to four people work together on the same repair.

One repairer can fix cars in an average time of 30 minutes. The addition of a person on the team reduces the repair time by 5 minutes. While these cars are down, lost income is $40 per hour. Cars tend to break down at the rate of three per hour.

How many repairers should be hired?