R(x)=80 x is the revenue function for the sale of x...

$R(x)=80 x$ is the revenue function for the sale of $x$ bicycles, in dollars. The cost to manufacture $x$ bikes, in dollars, is $C(x)=60 x+7000$. a) Find the profit function, $P(x),$ that describes the manufacturer's profit from the sale of $x$ bicycles. b) What is the profit from the sale of 500 bicycles?

$R(x)=80 x$ is the revenue function for the sale of $x$ bicycles, in dollars. The cost to manufacture $x$ bikes, in dollars, is $C(x)=60 x+7000$.
a) Find the profit function, $P(x),$ that describes the manufacturer's profit from the sale of $x$ bicycles.
b) What is the profit from the sale of 500 bicycles?

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Key Concepts

Revenue Function

A revenue function represents the total income generated from selling goods or services, typically calculated by multiplying the number of units sold by the selling price per unit. It is essential in financial analysis to understand how changes in sales volume affect overall income.

Cost Function

A cost function expresses the total expenditure incurred in the production or sale of goods, including both fixed costs, which do not vary with output, and variable costs, which do. It provides insight into the resources consumed in operations and is vital for budgeting and pricing.

Profit Function

A profit function is derived by subtracting the total cost function from the revenue function. It measures the net income or loss and is key for assessing the financial performance of a business or project.

Function Evaluation

Function evaluation involves substituting specific values into a function to compute an outcome, such as determining the profit for a given quantity of goods sold. This process is fundamental in applying mathematical models to real-world scenarios.

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