A city is considering building a new recreation center in a location at which more houses have been recently built and the existing centers are too...

A city is considering building a new recreation center in a location at which more houses have been recently built and the existing centers are too far to serve that part of the community. The center will include different exercise equipment, courts, and programs. The cost of building the center and acquiring the necessary equipment is $950,000. However, $450,000 will come in the form of equipment that will be donated by local businesses in return of having have their signs displayed around the center. The annual cost of consumables and bills (water, electricity, towels, supplies, etc) is $80 per member and the center plans to charge a monthly membership fee of $70. Ignoring depreciation and time value of money, answer the following and show your work:

1. How many members does the center have to have at the end of the second year if the city will be satisfied to get back the money it invested at the end of the second year. Note that donated money for equipment is not part of the investment.

2. If the center doubles its break-even membership in the third year, how much profit will it make in that year?

3. If the number of members in part (1) turns out to be too high to be realistic and only half of that number is attainable, how much in membership fees does the center need to charge to still break-even at the end of the second year?