Problem:

A private prisoner-transfer facility would lease for $50,000 per year, which the county is considering to lease. The country estimates it will cost $50 per prisoner to process the paperwork at this new location. The county is paid a $75 commission for each new prisoner it processes. If its holding area at this new location has design and effective capacities of 10,000 and 7,500 prisoners processed annually, respectively, and it plans to be 80% efficient in its use of this space.

Required:

Question 1) How many prisoners does the county plan to process per year?

Solve the problem and show all work.