Question

The Audubon Society at Enormous State University (ESU) is planning its annual fund raising "Eat-a-thon." The society will charge students 87 per serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at 17€ per serving, and the $350 cost of renting the facility for the evening. (a) Write down the associated cost function C(x) in dollars. C(x) Write down the revenue function R(x) in dollars. R(X) Write down the profit function P(x) in dollars. P(x) (b) How many servings of pasta must the Audubon Society sell to break even? servings (c) What profit (or loss) results from the sale of 1,500 servings of pasta?

Answer 1

a) Cost

`C(x)=0.17x +350`

Revenue

`R(x)=0.87x`

Profit

`P(x)=0.7x-350`

b) 500 servings

c) $ 700 dollars

Explanation:

a) The total cost is the cost per serving plus the cost of renting the facility

Cost per serving = 0.17 per serving

Cost of renting = 350

and we write:

`C(x)=0.17x +350`

The total revenue is the what the University charges per serving, which is 87 cents per serving. And we write:

`R(x)=0.87x`

Profit is Revenue minus Cost, which is:

`P(x)= R(x)-C(x)=0.87x-(0.17x +350)= 0.87x -0.17x -350= 0.7x - 350\\\\P(x)=0.7x-350`

b) To break even Revenue equals Cost, we write

`R(x)=C(x)\\0.87x=0.17x+350\\0.87x -0.17x=350\\0.7x=350\\x=(350)/(0.7) =500`

500 servings must the Audubon Society sell to break even.

c) we plug 1,500 into the P(x) equation and we get:

`P(x)=0.7x-350\\P(1,500)=0.7(1,500)-350\\P(1,500)=0.7(1,500)-350\\P(1,500)=1,050-350\\P(1,500)=700`

The sale of 1,500 servings of pasta results in a profit of $ 700 dollars.