A boathouse costs $2200 a month to operate, and it spends $550 each

month for every boat that it docks. The boathouse charges a monthly fee of

$850 to dock a boat. If n is the number of boats, which equation represents

the profit function of the boathouse?

A. p=300n-2200

B. p=850n-2200

C. p=300n+2200

D. p=2200n+300

Answer A: 300 n - 2200

Step-by-step explanation:

The profit function will be the income minus the cost of maintaining the boathouse.

The income comes from the number of boats that it docks (n), times the monthly fee that each boat pays ($850), That is:

Income = 850 n

Now the monthly cost to operate the boathouse is the fix $2200 cost plus $550 per boat. That is:

2200 + 550 n

Now, the difference "Income - Cost" that defines the profit function becomes:

850 n - {2200 + 550 n} = 850 n - 550 n - 2200 = 300 n - 2200