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

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

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

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Key Concepts

Evaluating Functions at Specific Points

This concept involves substituting a particular value into a function to calculate the corresponding output. It is an important tool for determining specific outcomes, such as the profit resulting from a given number of units sold.

Revenue Function

A revenue function represents the income a business generates from selling goods or services. It is typically modeled as a function of the number of units sold, where increases in the sales volume lead to proportional increases in total revenue.

Cost Function

A cost function calculates the total expenses incurred in the production process, comprising both variable costs (which change with the level of production) and fixed costs (which remain constant regardless of production volume). This function is essential for understanding and managing a business's expenditures.

Profit Function

The profit function is derived by subtracting the cost function from the revenue function and represents the financial gain or loss from production and sales. This function helps determine how different levels of sales affect overall profitability.

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