Question

The total cost (in dollars) of producing x college textbooks is C(x)=46x+24,000. a)what are the fixed costs? b)what is the marginal cost per book?c)what is the total cost of producing 500 books?33,000 books? d) what is the average cost when 500 books are produced? When 33,000 books are produced?

Answer 1

ANSWER:

a) $24000

b) $46

c) $47000, $1542000

d) $94, $46.73

STEP-BY-STEP EXPLANATION:

We have the following function:

$C\mleft(x\mright)=46x+24000$

a)

The fixed cost is the y-intercept of the function, therefore:

24000

b)

The marginal cost is the cost associated with a book, that is, the slope of the function, therefore:

46

c)

We calculate the total cost like this:

$\begin{gathered} C(500)=46\cdot500+24000=47000 \\ C(33000)=46\cdot33000+24000=1542000 \end{gathered}$

d)

We calculate the average cost like this:

$\begin{gathered} ac=\frac{C\mleft(x\mright)}{x} \\ \frac{C(500)}{500}=\frac{47000}{500}=94 \\ \frac{C(33000)}{33000}=\frac{1542000}{33000}=46.73 \end{gathered}$