Profit function

Definition

A profit function represents the relationship between a business's profit and its sales or production levels. It is typically expressed as $P(x) = R(x) - C(x)$, where $R(x)$ is the revenue function and $C(x)$ is the cost function.

5 Must Know Facts For Your Next Test

1. Profit functions are often linear or quadratic in algebraic problems involving two variables.
2. The break-even point occurs where the profit function equals zero, i.e., total revenue equals total cost.
3. Maximizing profit involves finding the vertex of a quadratic profit function when applicable.
4. Graphing profit functions can help visualize how changes in production affect profitability.
5. Solving systems of equations can determine optimal production levels for maximizing profits.

Review Questions

• How do you express a profit function using revenue and cost functions?
• What does it mean to find the break-even point on a graph of a profit function?
• How can solving systems of equations help in maximizing profits?

Related terms

Revenue Function: An equation that calculates total income from sales, typically expressed as $R(x) = p \cdot x$, where $p$ is price per unit and $x$ is quantity sold.

Cost Function: An equation representing total costs incurred by a business, often denoted as $C(x) = F + Vx$, where $F$ is fixed costs and $V$ is variable cost per unit.

Break-Even Point: The level of production at which total revenues equal total costs, resulting in zero profit.