Question

The average cost for printing copies of a self published paperback book with Company A is c(x)=120+4x/x

The average cost for printing x copies of a paperback book with Company B is d(x)=25+10x/2x

1. Which company would you recommend to an author who wants to print 10 books? Explain your reasoning.

2. Which company would you recommend to an author who thinks their book will be a best seller and needs to print thousands of books? How could you rewrite the equations to make the choice clearer?

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Answer 1

The true statements are:

• You would recommend company B to an author who wants to print 10 books
• You would recommend company A as the bestseller to print thousand books;

What are functions?

Functions are equations that are used to represent relations and ordered pairs

The average cost functions of both companies are given as:

• Company A: $c(x) = \frac{120 + 4x}{x}$
• Company B: $d(x) = \frac{25 + 10x}{2x}$

(a) The average cost to print 10 books

This means that x = 10.

The average costs for both companies are calculated as follows:

$c(10) = \frac{120 + 4 \times 10}{10}$

$c(10) =16$

$d(10) = \frac{25 + 10 \times 10}{2 \times 10}$

$d(10) = 6.25$

By comparison:

$6.25 < 16$

Hence, you would recommend company B to an author who wants to print 10 books;

This is so, because company B has a lower average value when x = 10

(b) Bestseller for thousands of books

We have:

• Company A: $c(x) = \frac{120 + 4x}{x}$
• Company B: $d(x) = \frac{25 + 10x}{2x}$

Simplify both equations

$c(x) =\frac{120}{x} + 4$

$d(x) =\frac{25}{2x} + 5$

The constant value in function c(x) is less than the constant value in function d(x)

i.e. 4 < 5

Hence, you would recommend company A as the bestseller to print thousand books;

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