Chapter 7.6, Problem 60E

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 Trekker shoe company is planning to manufacture a new line of workout “toe shoes.” Fixed costs will be $\$266,000$ and it will cost $\$30$ to produce each pair of shoes. The shoes will sell for $\$125$ a pair.