The YMCA rents low-cost rooms as an alternative to expensive hotels. It charges $ 10 per night for a dormitory room (Shared with many others) or $20 per night for a small private room. Generally, three-quarters of their guest rent dormitory room. The variable cost for a dormitory room is $ 4 per night. The average cost for a private room is $6 per night. There are fixed cost of $100,000 per year related to the room (e.g., desk clerk, rent, heat).
a. How many people must stay at the YMCA every year for it to break even?
b. How many people will be in private rooms at the break-even point?