The total cost in dollars of producing x college textbooks i

The total cost (in dollars) of producing x college textbooks is C(x) = 40x + 45,000.

(a) What are the fixed costs?

(b) What is the marginal cost per book?

(c) What is the total cost of producing 1100 books? 32,000 books?

(d) What is the average cost when 1100 books are produced? when 32,000 books are produced?

Solution

C(x) = 40x + 45,000.

a)

here C(x) can be divided in two parts

fixed cost and variable cost

40x is variable cost and 45000 is fixed cost.

b)

marginal cost is derivative of cost function. so

marginal cost= d(c)/dx=40

c)

cost of producing 1100 books= 40*1100+45000=89000

cost of producing 32000 books= 40*32000+45000=1325000

d)

average cost is c(x)/x

so average cost when 1100 books prosuced= 89000(total cost in producing 1100 books)/1100

=80.91

average cost for 32000 books= 1325000/32000=41.41