Chapter 4.1, Problem 69E

Break-even analysis. A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, etc.) of $\text{\$}48,000$ per day and variable costs (labor, materials, etc.) of $\text{\$}48,000$ per unit produced. The mowers are sold for $\text{\$}1,800$ each. So the cost and revenue equations are

$\begin{array}{cc}y=48,000+1,400x& \text{Cost}\text{equation}\\ y=1,800x& \text{Revenue equation}\end{array}$

where $x$ is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars.

(A) How many units must be manufactured and sold each day for the company to break even?

(B) Graph both equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.