A company that sells radios has yearly fixed costs of ...

A company that sells radios has yearly fixed costs of $\$ 600,000 .$ It costs the company $\$ 45$ to produce each radio. Each radio will sell for $\$ 65 .$ The company's costs and revenue are modeled by the following functions, where $x$ represents the number of radios produced and sold: $C(x)=600,000+45 x$ This function models the company's costs. $R(x)=65 x$ This function models the company's revenue. Find and interpret $(R-C)(20,000),(R-C)(30,000),$ and $(R-C)(40,000)$

A company that sells radios has yearly fixed costs of $\$ 600,000 .$ It costs the company $\$ 45$ to produce each radio. Each radio will sell for $\$ 65 .$ The company's costs and revenue are modeled by the following functions, where $x$ represents the number of radios produced and sold:
$C(x)=600,000+45 x$
This function models the company's costs. $R(x)=65 x$
This function models the company's revenue.
Find and interpret $(R-C)(20,000),(R-C)(30,000),$ and $(R-C)(40,000)$

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Key Concepts

Break-even Analysis

Break-even analysis identifies the point where total revenue equals total costs, meaning the company neither makes a profit nor incurs a loss. This analysis is essential for understanding the minimum sales volume required to cover fixed and variable costs.

Revenue Function

The revenue function calculates the total income a company generates from selling its products, typically modeled as the product of the selling price per unit and the number of units sold.

Cost Function

The cost function represents the total costs incurred by a company in producing a certain number of units, combining fixed costs that remain constant regardless of output and variable costs that increase with each produced unit.

Profit Function

The profit function, found by subtracting the cost function from the revenue function, measures the net earnings from production. It indicates whether the operation is making a profit or incurring a loss at a given level of production.

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