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(19. Break-Even Analysis Your college newspaper, The Colle giate Investigator, has fixed production costs of 70 per edi- tion and marginal printing and distribution costs of 40phi per copy. The Collegiate Investigator sells for 50phi per copy. a. Write down the associated cost, revenue , and profit functions. HINT (See Examples 1 and 2.] b. What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? c. How many copies should be sold in order to break even?

Pergunta

(19. Break-Even Analysis Your college newspaper, The Colle
giate Investigator, has fixed production costs of 70 per edi-
tion and marginal printing and distribution costs of 40phi  per
copy. The Collegiate Investigator sells for 50phi  per copy.
a. Write down the associated cost, revenue , and profit
functions. HINT (See Examples 1 and 2.]
b. What profit (or loss) results from the sale of 500 copies
of The Collegiate Investigator?
c. How many copies should be sold in order to break even?

(19. Break-Even Analysis Your college newspaper, The Colle giate Investigator, has fixed production costs of 70 per edi- tion and marginal printing and distribution costs of 40phi per copy. The Collegiate Investigator sells for 50phi per copy. a. Write down the associated cost, revenue , and profit functions. HINT (See Examples 1 and 2.] b. What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? c. How many copies should be sold in order to break even?

Solução

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RicardoVeterano · Tutor por 9 anos

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a. Let's define the cost, revenue, and profit functions for The Collegiate Investigator.

Cost function (C(x)):
The cost function represents the total cost of producing x copies of the newspaper. It includes the fixed production costs and the marginal printing and distribution costs per copy.
C(x) = Fixed production costs + Marginal cost per copy * Number of copies
C(x) = 70 +
40x

Revenue function (R(x)):
The revenue function represents the total revenue generated from selling x copies of the newspaper.
R(x) = Selling price per copy * Number of copies
R(x) = 50x Profit function (P(x)): The profit function represents the profit or loss resulting from selling x copies of the newspaper. It is calculated as the difference between the revenue and the cost. P(x) = R(x) - C(x) P(x) =
50x - (70 +
40x)
P(x) = 50x -
70 - 40x P(x) =
10x - 70 b. To find the profit or loss from the sale of 500 copies of The Collegiate Investigator, we need to substitute x = 500 into the profit function. P(500) =
10(500) - 70 P(500) =
5000 - 70 P(500) =
4930

Therefore, the profit resulting from the sale of 500 copies of The Collegiate Investigator is 4930. c. To find the break-even point, we need to find the number of copies that would result in a profit of
0. This means that the revenue and the cost are equal.

To find the break-even point, we set the profit function equal to 0 and solve for x.
10x - 70 =
0
10x =
70
x = 7

Therefore, The Collegiate Investigator needs to sell 7 copies in order to break even.
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