A company's revenue, R(x) in dollars, from the sale of x dog...

A company's revenue, $R(x)$ in dollars, from the sale of $x$ dog houses is given by $R(x)=60 x$. The company's cost, $C(x)$ in dollars, to produce $x$ dog houses is $C(x)=45 x+6000$. a) Find the profit function, $P(x),$ that describes the company's profit from the sale of $x$ dog houses. b) What is the profit from the sale of 300 dog houses?

A company's revenue, $R(x)$ in dollars, from the sale of $x$ dog houses is given by $R(x)=60 x$. The company's cost, $C(x)$ in dollars, to produce $x$ dog houses is $C(x)=45 x+6000$.
a) Find the profit function, $P(x),$ that describes the company's profit from the sale of $x$ dog houses.
b) What is the profit from the sale of 300 dog houses?

Key Concepts

Profit Function

A profit function calculates the financial gain obtained from a business operation by subtracting the total costs from the total revenue. It is a fundamental concept in economics and business, as it helps in understanding how sales volume, pricing, and cost management contribute to overall profitability. Establishing the profit function is key to making informed business decisions.

Revenue Function

A revenue function represents the total amount of money generated from the sale of goods or services. It maps the quantity sold to the income received, usually based on a price per unit. In economic modeling, this function is essential for understanding how sales volume influences income and for setting benchmarks to cover associated costs.

Cost Function

A cost function outlines the total expense incurred in the production of goods or services. It typically includes both variable costs (which change with the quantity produced) and fixed costs (which remain constant regardless of production level). This concept is crucial in analyzing how production levels impact overall expenditure and in determining profitability.

Linear Functions

Linear functions are mathematical functions that create a straight-line graph when plotted. They are used to model relationships with a constant rate of change, such as the proportional relationship between the number of goods sold and the revenue generated or costs incurred. In business applications, linear functions simplify analysis and forecasting when changes occur at a constant rate.

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