Question

A group is planning its annual fund-raiser in which it raises money by selling pasta dinners. The group will charge $2.21 per serving of pasta. The expenses the group will incur are the cost of the pasta, $0.44 per serving, and the $318 cost of renting the facility for the evening. Find the associated cost, revenue, and profit function. What will be the resulting profit if they sell 99 servings of pasta? (Round to the nearest cent which is two decimal places. Do not include units or symbols.)

Answer 1

The cost is given by
`C(n) = 318 + 0.44n`.

The revenue is given by
`R(n) = 2.21n`.

The profict is given by:
`P(n) = 1.77n - 318`

The resulting profit if they sell 99 servings of pasta is of -$142.77, that is, there is a loss of $142.77.

Explanation:

Cost:

The expenses the group will incur are the cost of the pasta, $0.44 per serving, and the $318 cost of renting the facility for the evening.

This means that the cost of n servings is given by:

`C(n) = 318 + 0.44n`

Revenue:

The group will charge $2.21 per serving of pasta.

This means that the revenue of selling n servings is given by:

`R(n) = 2.21n`

Profit:

The profit is given by the cost subtracted by the revenue. So

`P(n) = R(n) - C(n)`

`P(n) = 2.21n - (318 + 0.44n)`

`P(n) = 2.21n - 0.44n - 318`

`P(n) = 1.77n - 318`

What will be the resulting profit if they sell 99 servings of pasta?

This is P when
`n = 99`. So

`P(99) = 1.77*99 - 318 = -142.77`

The resulting profit if they sell 99 servings of pasta is of -$142.77, that is, there is a loss of $142.77.