The profit of a company is obtained by subtracting its cost...

The profit of a company is obtained by subtracting its cost from its revenue. In Exercises 87 and $88, R(x)$ represents the company's revenue when selling $x$ items and $C(x)$ represents the company's cost when producing $x$ items. a) Determine a profit function $P(x)$. b) Evaluate $P(x)$ when $x=100$.$R(x)=2 x^{2}-60 x$ $C(x)=8050-420 x$

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Key Concepts

Profit Function

The profit function represents the net gain or loss made by a company and is defined as the difference between the revenue function and the cost function. It is a fundamental concept in business mathematics that helps in determining how variations in production or sales volume affect profitability.

Revenue Function

The revenue function models the total income generated from the sale of goods or services as a function of the number of items sold. It is essential for understanding the earning potential of a business based on different sales volumes.

Cost Function

The cost function represents the total expenses incurred in producing a certain number of items. It includes both fixed and variable costs and is crucial for analyzing and managing the financial performance of a production process.

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine the corresponding output. This technique is widely used in mathematical modeling and analysis to assess the behavior of functions at particular points, such as determining profit at a specific production level.

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