posted by cindy .
Ettenheim village is considering building a town swimming pool. The annual facility cost would be $200,000. Staff salaries for the pool, which would only be open during the summer would be $75,000. Other fixed cost would be $20,000 a year. There are other expenses of $50 per person per season.
Marketing studies suggest that the village residents would be willing to spend $150 a year for an individual membership and $300 for family membership. On average families in the village have 3 people. How many members will have to join each year to make the pool cover its cost. Assume that 75% of the memberships are family memberships
Let N be the number of members. The annual revenue from memberships will be
(0.75N)x150 + (0.25N)x300 = 187.5 N
Add up the annual costs, which look to me like
295,000 + 50 N,
set that equal to 187.5 N and solve for N. That will give you the break-even value of N.