Question

An Ontario county is considering whether to pay $50,000 per year to lease a prisoner transfer facility in a prime location near Winnipeg., They estimate 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 they process. How many prisoners would they have to process annually to make a profit of $100,000 at this new location?

Answer 1

To make a profit of $100,000 at the new location, the Ontario county would need to process 2,000 prisoners annually.

Step-by-step explanation:

To determine the number of prisoners the Ontario county would have to process annually to make a profit of $100,000 at the new location, we need to consider the costs and revenue associated with processing each prisoner.

The county pays $50,000 per year to lease the facility and estimates it will cost $50 per prisoner to process the paperwork. On the other hand, they receive a $75 commission for each new prisoner they process.

Let's denote the number of prisoners they need to process as 'x'. The total cost to process the prisoners would be $50x (considering a cost of $50 per prisoner). The total revenue from processing the prisoners would be $75x (considering a commission of $75 per prisoner).

To make a profit of $100,000, the total revenue must exceed the total cost by $100,000. Therefore, we can set up the following equation: $75x - $50x = $100,000. Solving this equation, we find that x = 2,000.

Therefore, the Ontario county would need to process 2,000 prisoners annually to make a profit of $100,000 at the new location.