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:
If the center doubles its break-even membership in the third year, how much profit will it make in that year?
Please explain and show all work.