If northeastern operates in the phoenix$-$las vegas route, its aircraft for that route will be idle between midnight and $6$ am$.$ The airline is considering offering a red$-$eye special that would leave phoenix daily at midnight and return at $6$ am$.$ The marketing division estimates that if the fare were no more than $$20,$ at least $60$ new passengers would be attracted to each red$-$eye flight. Operating costs would be at the same rate for those flights, but advertising costs of the $$1,225$ per week would be required to promote the service. No food or beverage costs would be borne by the company. Assume the marketing division's estimates are correct. What is the minimum fare that would be required to break even on the red$-$eye?