Chapter 4.1, Problem 71E

In business, a company’s break-even point is the point at which the costs of production of a product will be equal to the amount of revenue from the sale of the product. In Problems 71–74, solve the system of equations by graphing to find the number of units that need to be produced for the company to break even.

71. Producing T-Shirts The San Diego T-Shirt Company designs and sells T-shirts for promoters to sell at music concerts. The cost y (in dollars) to produce x T-shirts is given by the equation y = 15x + 1000, and the revenue y (in dollars) from the sale of these T-shirts is y = 25x. Find the breakeven point: the point where the line that represents the cost, y = 15x + 1000, intersects the revenue line, y = 25x. Interpret the x-coordinate and the y-coordinate of the break-even point.