Break-Even Analysis in Functions
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Break-Even Analysis in Functions

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@FortuitousDeStijl

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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.

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