Answered

Suppose you create a graph of the cost function, [tex]C = 20n + 500[/tex], of a new bookstore, and you also graph the revenue function, [tex]R = 25n[/tex], where [tex]n[/tex] is the number of books sold. On your graph, would the point [tex]n = 100[/tex] be in the loss section, the profit section, or the break-even section?

A. Break-even section
B. Profit section
C. Loss section
D. You can't tell.



Answer :

GinnyAnswer
To determine whether the point [tex]\( n = 100 \)[/tex] falls into the loss, profit, or break-even section, we need to evaluate both the cost function and the revenue function at [tex]\( n = 100 \)[/tex] and then compare the values.

1. Cost Function Evaluation:
The cost function [tex]\( C \)[/tex] is given by:
[tex]\[ C = 20n + 500 \][/tex]
Substituting [tex]\( n = 100 \)[/tex] into the cost function:
[tex]\[ C = 20 \times 100 + 500 = 2000 + 500 = 2500 \][/tex]

2. Revenue Function Evaluation:
The revenue function [tex]\( r \)[/tex] is given by:
[tex]\[ r = 25n \][/tex]
Substituting [tex]\( n = 100 \)[/tex] into the revenue function:
[tex]\[ r = 25 \times 100 = 2500 \][/tex]

3. Comparison:
Now, we compare the cost [tex]\( C \)[/tex] and the revenue [tex]\( r \)[/tex]:
[tex]\[ C = 2500, \quad r = 2500 \][/tex]
Since [tex]\( C = r \)[/tex], the bookstore is neither making a profit nor incurring a loss; they are at the break-even point.

Therefore, at [tex]\( n = 100 \)[/tex], the point would be in the:

A. Break-even section