Download Your college newspaper, The Collegiate Investigator

Your college newspaper, The Collegiate Investigator, has fixed
production costs of $70 per edition and marginal printing and
distribution costs of 40¢ per copy. The Collegiate Investigator
sells for 50¢ per copy.
a) Write down the associated cost, revenue, and profit
functions.
Solution: The cost function has the form 𝐶 (𝑥 ) = 𝑚𝑥 + 𝑏,
where 𝑚 is the marginal cost (cost per item) and 𝑏 is the fixed
cost. It costs 40¢ per copy plus fixed costs of $70, so the cost
function is 𝐶 (𝑥 ) = 0.40𝑥 + 70.
Revenue is how much money is brought in. You find it by
multiplying the price of the item by the number of items you
sell, so Revenue = (price) × (quantity). In this case the price
you sell the newspapers for is 50¢, and 𝑥 stands for the
quantity that you sell. Thus, 𝑅(𝑥 ) = 0.50𝑥.
Profit is revenue minus cost, so
𝑃(𝑥 ) = 𝑅(𝑥 ) − 𝐶 (𝑥 ) = 0.50𝑥 − (0.40𝑥 + 70) = 0.10𝑥 − 70.
b) What profit (or loss) results from the sale of 500 copies of
The Collegiate Investigator?
Solution: Plug 500 into the profit function, which gives
𝑃(500) = 0.10(500) − 70 = −20, so selling 500 copies results
in a loss of $20.
c) How many copies should be sold in order to break even?
To find the break-even point, set the profit function equal to 0
and solve for 𝑥. This gives 0.10𝑥 − 70 = 0, so 0.10𝑥 = 70 and
𝑥 = 700. Thus, they must sell 700 copies to break even.