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Break-Even Analysis in Functions

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Questions and Answers

What distinguishes the dependent and independent variables in a function?

Both variables can be affected by external factors.

The dependent variable can change independently of the independent variable.

The dependent variable is always greater than the independent variable.

The independent variable's value determines the dependent variable's value. (correct)

In the break-even analysis, when does a company reach a break-even point?

When total revenue equals total cost. (correct)

When total profit is at its maximum.

When total costs are greater than total revenue.

When fixed costs are negligible.

What does the total cost function C(x) include?

Fixed costs plus variable costs associated with production. (correct)

Only fixed costs without any production costs.

Only variable costs associated with production.

Total revenue generated from the sales only.

What is the formula for total profit P(x)?

<p>P(x) = R(x) - C(x)</p> Signup and view all the answers

Study Notes

Functions

Variables are used to represent numerical values in a function.
Dependent variable (y) is determined by the value of the independent variable (x).

Break-Even Analysis

Total cost function: Represents the total cost of production.
- Fixed cost: Remains constant regardless of the number of units produced.
- Variable cost: Varies depending on the number of units produced.
Total revenue function: Represents the total income generated from sales.
- Price: The selling price per unit.
- Quantity sold: The number of units sold.
Total profit function: Represents the difference between total revenue and total cost.
Break-even point: Occurs when the total cost equals the total revenue, resulting in zero profit.

Exercise

Selling price per unit: 75 pounds
Fixed cost: 210,000 pounds
Variable cost per unit: 5 pounds
Break-even point: The number of units that need to be sold to cover all costs.
Profit: The difference between total revenue and total cost.

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Description

This quiz focuses on understanding the break-even analysis using functions related to cost, revenue, and profit. Learn about the roles of fixed and variable costs in determining the break-even point and the implications of selling price and quantity sold on profitability.