A company that sells radios has a yearly fixed cost of ...

A company that sells radios has a yearly fixed cost 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: $C(x)=600,000+45 x$ 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 a yearly fixed cost 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:
$C(x)=600,000+45 x$ 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 $(R-C)(40,000)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cost Function

A cost function models the total expenses incurred in producing goods or services. It typically includes both fixed costs, which remain constant regardless of the level of production, and variable costs, which depend directly on the number of units produced. This function helps businesses understand how costs behave with changing production levels.

Revenue Function

A revenue function represents the total income generated from selling products or services. It is generally modeled as the product of the selling price per unit and the number of units sold. This function is crucial for predicting income and planning sales strategies.

Profit Function

The profit function is derived by subtracting the cost function from the revenue function, indicating the net gain or loss from operations. It provides insight into the financial performance of a company as production volume changes, helping determine break-even points and profitability.

Function Evaluation

Function evaluation involves substituting specific values into a function to calculate an output. In the context of business models, evaluating the profit function for specific production quantities allows one to assess the expected profit (or loss) for those production levels, leading to informed decision-making.

Transcript

Please give Ace some feedback