$2-11$ The Country Fields Retirement Community charges $$\frac{6000}{?}$ month for a single senior citizen to reside in an efficiency apartment with assisted living care. The facility has operating expenses of $$600,000$ per month. Staffing levels are dependent on the number of residents. Each senior who enters the community requires additional food, personal care, and support staff time. The estimated cost for each person is $$4000$ per person per month.

$($a$)$ How many senior citizen residents does the facility need to have in order to reach the breakeven point?

$($b$)$ What is the company's annual profit or loss if they maintain an average residency level of $350$ senior citizens?

Contributed by Gillian Nicholls, Southeast Missouri State University