Final answer:
Upon calculating the average costs for printing 100 books, company A offers a price of $124 while company B offers a significantly lower price of $30. It is therefore recommended to print with company B for a more economical option.
Step-by-step explanation:
To compare the costs of printing 100 books with company A and company B, we need to plug in the value of x=100 into each company's cost function and then calculate the average cost per book.
For company A, the cost function is given as c(x) = 120 + (4x) / x. Plugging in x=100, we get:
c(100) = 120 + (4×100) / 100
c(100) = 120 + 400 / 100
c(100) = 120 + 4
c(100) = 124
Therefore, the average cost for printing 100 books with company A is $124.
For company B, the cost function is given as D(x) = 25 + (10x) / (2x). Plugging in x=100, we get:
D(100) = 25 + (10×100) / (2×100)
D(100) = 25 + 1000 / 200
D(100) = 25 + 5
D(100) = 30
Therefore, the average cost for printing 100 books with company B is $30.
Based on the calculations, it is more economical to print 100 books with company B, as the average cost is significantly lower.