Question

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 1

Answer A: 300 n - 2200

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