Unlocking Profit: Cost, Revenue, and Break-Even Analysis

Algebra 2 Grades High School 4:26 Video
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Lesson Description

Learn how to model real-world business scenarios using cost, revenue, and profit equations. Discover how to find the break-even point to make informed decisions.

Video Resource

Cost, Revenue, Profit Equations and Break Even Point

Mario's Math Tutoring

Duration: 4:26
Watch on YouTube

Key Concepts

  • Cost Function (Fixed and Variable Costs)
  • Revenue Function (Price per unit * Quantity)
  • Profit Function (Revenue - Cost)
  • Break-Even Point (Cost = Revenue or Profit = 0)

Learning Objectives

  • Students will be able to define and differentiate between cost, revenue, and profit.
  • Students will be able to create equations to model cost, revenue, and profit from word problems.
  • Students will be able to calculate the break-even point by setting cost equal to revenue or profit equal to zero.
  • Students will be able to interpret the meaning of the break-even point in a business context.

Educator Instructions

  • Introduction (5 mins)
    Briefly introduce the concepts of cost, revenue, and profit in a business context. Explain the importance of understanding these concepts for making informed financial decisions. Show a brief real-world example, such as starting a lemonade stand, to illustrate the basic idea.
  • Video Presentation (15 mins)
    Play the Mario's Math Tutoring video: 'Cost, Revenue, Profit Equations and Break Even Point'. Instruct students to take notes on key definitions, formulas, and the example problem presented in the video.
  • Guided Practice (15 mins)
    Work through a similar example problem as a class, guiding students through each step of creating the cost, revenue, and profit equations and then solving for the break-even point. Encourage student participation and address any questions or misconceptions.
  • Independent Practice (10 mins)
    Provide students with a new word problem and have them work individually to create the equations and find the break-even point. Circulate to provide assistance and answer questions.
  • Review and Wrap-up (5 mins)
    Review the key concepts and formulas. Answer any remaining questions. Preview the upcoming lesson or assignment.

Interactive Exercises

  • Break-Even Point Challenge
    Divide students into small groups and provide each group with a different business scenario (e.g., a bakery, a car wash, a tutoring service). Have them create the cost, revenue, and profit equations for their scenario and determine the break-even point. Each group presents their findings to the class.

Discussion Questions

  • What are some examples of fixed costs and variable costs in a business?
  • How does the break-even point help a business owner make decisions?
  • What happens to profit if a company sells more units than its break-even point?
  • How would changes in fixed costs, variable costs, or selling price affect the break-even point?

Skills Developed

  • Algebraic Modeling
  • Problem Solving
  • Critical Thinking
  • Equation Solving
  • Real-world Application

Multiple Choice Questions

Question 1:

Which of the following is the correct formula for calculating profit?

Correct Answer: Profit = Revenue - Cost

Question 2:

The break-even point is where:

Correct Answer: Revenue equals cost

Question 3:

Fixed costs are costs that:

Correct Answer: Remain constant regardless of production

Question 4:

Variable costs are costs that:

Correct Answer: Increase with production

Question 5:

If a company's revenue is $5000 and its cost is $3000, what is the profit?

Correct Answer: $2000

Question 6:

The equation for revenue is typically represented as:

Correct Answer: Price per unit * Quantity

Question 7:

Which of these is an example of a fixed cost?

Correct Answer: Rent

Question 8:

What does 'n' typically represent in the cost, revenue, and profit equations?

Correct Answer: Number of units sold

Question 9:

If the profit equation is P = -2x + 100, where x is the number of units sold, what is the break-even point?

Correct Answer: x = 50

Question 10:

The purpose of finding the break-even point is to determine:

Correct Answer: The sales volume needed to cover all costs

Fill in the Blank Questions

Question 1:

The cost function includes both __________ costs and __________ costs.

Correct Answer: fixed, variable

Question 2:

__________ is the money a company earns from selling its products or services.

Correct Answer: Revenue

Question 3:

If the cost is $10 per unit and you sell 50 units, the revenue is $__________.

Correct Answer: 500

Question 4:

At the break-even point, the profit is always equal to __________.

Correct Answer: zero

Question 5:

The formula for profit is: Profit = Revenue - __________.

Correct Answer: Cost

Question 6:

Expenses that do not change with the number of items produced are called __________ costs.

Correct Answer: fixed

Question 7:

The point at which total revenue equals total cost is called the __________ point.

Correct Answer: break-even

Question 8:

When total revenue exceeds total cost, the company makes a __________.

Correct Answer: profit

Question 9:

If a company sells each widget for $5, the price per unit represents the __________.

Correct Answer: revenue

Question 10:

If fixed costs are $2000 and variable costs are $5 per unit, the cost function is C = 2000 + __________.

Correct Answer: 5x

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.1.7:Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used.

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