Use the equations for the total cost C and total revenue R...

Use the equations for the total cost $C$ and total revenue $R$ to find the number $x$ of units a company must sell to break even. (Round to the nearest whole unit.)
$$C=8650 x+250,000, \quad R=9502 x$$

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Key Concepts

Break-Even Analysis

Break-even analysis is the process of finding the point at which total revenues equal total costs. At the break-even point, the company makes neither profit nor loss, and this analysis helps in making important pricing and production decisions.

Cost Function

The cost function represents the total cost associated with producing and selling a certain number of units, usually comprising fixed costs that do not change with the level of production and variable costs that do. Understanding this function is crucial for determining the break-even point.

Revenue Function

The revenue function calculates the total income generated from selling a specific number of units, typically as the product of the unit price and the number of units sold. It is essential for assessing whether sales will cover costs.

Solving Linear Equations

Solving linear equations in this context involves setting the cost function equal to the revenue function and solving for the quantity of units sold. This mathematical approach is fundamental in determining the break-even quantity.

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