Question

A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given information

`\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }*\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}`

The function for the cost price becomes:

`61000+1.5x`

STEP 2: Get the function for the selling price

The function for the selling price becomes:

`\text{ \$}15x`

STEP 3: Calculate the number of books required to break even

To get the breakeven, the cost price will be equal to selling price. Therefore,

`\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ (61000)/(13.5)=(13.5x)/(13.5) \\ 4518.518519=x \\ x\approx4519 \end{gathered}`

Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519