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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 = 150[/tex] be in the loss section, the profit section, or the break-even section?

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



Answer :

GinnyAnswer
To determine whether the point [tex]\( n = 150 \)[/tex] is in the loss section, profit section, or break-even section for a new bookstore, we need to evaluate both the cost and revenue functions at [tex]\( n = 150 \)[/tex].

1. The cost function is given by:
[tex]\[ C = 20n + 500 \][/tex]
Substituting [tex]\( n = 150 \)[/tex]:
[tex]\[ C = 20 \times 150 + 500 = 3000 + 500 = 3500 \][/tex]

2. The revenue function is given by:
[tex]\[ r = 25n \][/tex]
Substituting [tex]\( n = 150 \)[/tex]:
[tex]\[ r = 25 \times 150 = 3750 \][/tex]

3. Now we compare the cost and revenue at [tex]\( n = 150 \)[/tex]:
- Cost at [tex]\( n = 150 \)[/tex] is 3500.
- Revenue at [tex]\( n = 150 \)[/tex] is 3750.

Since the revenue (3750) is greater than the cost (3500), the bookstore is making a profit at [tex]\( n = 150 \)[/tex].

Thus, the point [tex]\( n = 150 \)[/tex] would be in the:
D. Profit section

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