Chapter 7.6, Problem 59E

If a company produces and sells x units of a certain product, there will be a cost, C, of producing the product described by the equation

$\text{C}=\text{fixed cost}+\left(\text{cost per unit produced}\right)\cdot x$.

The revenue, R, is the amount of money that comes in from selling x units of the product and is described by the equation

$\text{R}=\left(\text{price per unit sold}\right)\cdot x$.

The point where C and R are equal is called the break-even point, and it tells us the point at which the company starts to make a profit. Find the break-even point for the situations described in Exercises 59 and 60.

Manufacturing. The EarBudz Company is planning to manufacture a new line of high-end noise-reduction ear buds. Fixed costs will be $\$126,000$ and it will cost $\$12$ to produce each pair of ear buds. The ear buds will sell for $\$40$ a pair.