Find the sales necessary to break even (R=C) for the cost C...

Find the sales necessary to break even $(R=C)$ for the cost $C$ of producing $x$ units and the revenue $R$ obtained by selling $x$ units. (Round your answer to the nearest whole unit.) See Example 6.
$C=2.65 x+350,000 ; R=4.15 x$

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Key Concepts

Revenue Function

The revenue function represents the total earnings from selling a number of units, calculated by multiplying the unit price by the number of units sold. This function is critical for comparing income against costs in order to determine profitability.

Solving Linear Equations

Solving linear equations involves setting two expressions equal to each other and isolating the variable to find its value. In the context of break-even analysis, it is used to determine the precise number of units required to equate revenue with costs.

Cost Function

The cost function models the total costs incurred in producing a certain number of units, typically expressed as a combination of fixed costs and variable costs. Fixed costs remain constant regardless of output while variable costs change in proportion to the number of units produced.

Break-even Analysis

Break-even analysis involves finding the point at which total revenue equals total costs, meaning there is no net profit or loss. It is a fundamental concept in business and economics that helps decision-makers understand how many units need to be sold to cover all costs.

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