Question

Your college newspaper, The Collegiate Investigator, has fixed production costs of $68 per edition and printing and distribution costs of 41¢ per copy. The Collegiate Investigator sells for 51¢ per copy.
a. Write down the associated cost function C(x) in dollars.
b. Write down the revenue function R(x) in dollars.
c. Write down the profit function P(x) in dollars.
d. What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator?
e. How many copies should be sold in order to break even?

Answer 1

Answer:

a. The cost function is $C(x)=0.41x+68$.

b. The Revenue function is $R(x)=0.51x$.

c. The profit function is $P(x)=0.1x-68$.

d. Selling 500 copies results in a loss of $18.

e. They must sell 680 copies to break even.

Step-by-step explanation:

a. A linear cost function may be expressed as fol­lows:

$C(x)=mx+b$

where $C(x)$ is the total cost, b is fixed cost and m is the variable cost.

It costs 41¢ per copy plus fixed costs of $68, so the cost function is

$C(x)=0.41x+68$

b. Revenue is equal to the number of units sold times the price per unit. To obtain the revenue function, multiply the output level by the price function.

The price you sell the newspapers for is 51¢, and x stands for the quantity that you sell. Thus,

$R(x)=0.51x$

c. The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.

$P(x)=R(x)-C(x)\\P(x)=0.51x-(0.41x+68)\\P(x)=0.1x-68$

d. Plug 500 into the profit function, which gives

$P(500)=0.1(500)-68\\P(500)=50-68=-18$

Selling 500 copies results in a loss of $18.

e. To find the break-even point, use the following formula

$Break-Even \:Point \:in \:Units=\frac{Fixed \:Costs}{Price \:of \:Product - Variable \:Costs} \\\\Break-Even \:Point \:in \:Units=\frac{68}{0.51-0.41}=\frac{68}{0.1}=680$

They must sell 680 copies to break even.