MA.912.FL.2.2

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Solve real-world problems involving profits, costs and revenues using spreadsheets and other technology.

Examples

Example: A travel agency charges $2400 per person for a week-long trip to London if the group has 16 people or less. For groups larger then 16, the price per person is reduced by $100 for each additional person. Create an expression describing the revenue as a function of the number of people in the group. Determine the number of people that maximizes the revenue.

Clarifications

Clarification 1: Instruction includes the connection to data. 

Clarification 2: Instruction includes displaying profits and costs over time in a table or graph and using the graph to predict profits. 

Clarification 3: Problems include maximizing profits, maximizing revenues and minimizing costs.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Financial Literacy
Standard: Develop an understanding of basic accounting and economic principles.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Data

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

In middle grades and Algebra I, students have worked with data using tables and graphs to solve real-world problems. In Math for Data and Financial Literacy, students utilize their understanding of data, tables, and graphs to predict profits and solve problems related to maximizing profits, maximizing revenues and minimizing costs. 
  • Throughout instruction, it will be important to help students connect the mathematical concepts to everyday experiences (MTR.7.1) as they validate conclusions by comparing them to a given situation. 
  • The following terms are used for the application of this benchmark:

 

  • During instruction, students will need to gain understanding of expenses and the types of expenses. Expenses can be variable or fixed. The Expense function is E = V + F with E representing total expenses, V representing variable expenses and F representing fixed expenses. 
    • For example, when a company makes a product it has fixed expenses, such as equipment or real estate, and variable expenses, such as labor and materials. These expenses can be variable because the number of items can be variable. So, the typical formula for expenses, E, can be found by the product of the number of items, q, and the cost per item, c, plus the fixed expenses, f, which can be represented by the equation E = qc + f. 
  • Using the understanding of expenses and revenue, instruction will include determining the difference between revenue and expenses to determine the profit or loss. 
    • For example, if a company has a manufacturing cost per item of $53 and sells that item for p dollars, and the company a has fixed cost of $2750 per month, then the expression for the monthly profit, P, could be represented as P = pq − 53q − 2750 which is equivalent to P = q(p − 53) − 2750. 
  • Instruction includes understanding the relationship between the price per item, p, and the demand for that item, which is the number of items, q, that can be sold at that price. This relationship is called the demand function. In the simplest case, the demand function is a linear function. 
    • For example, a company determines that the demand function for its product is q = 1500 − 10p. So, one can determine that the maximum demand (y-intercept) is 1500 because that is the demand when the price of the product is $0. There will be no demand for the product (x-intercept) when the price is $150. 
    • For example, if the monthly profit of a product is represented by the expression q(p − 53) − 2750 and the demand function is q=1500 − 10p, then the monthly profit, P, can be represented as a function of p: P = (1500 − 10p)(p − 53) − 2750. The company can maximize its monthly profit by choosing the price, p, corresponding to the vertex of this quadratic function. 
  • Students may need to verify the reliability of solutions and determine if the overall profit is correct based on revenue.

 

Common Misconceptions or Errors

  • Students may need support in working with formulas or solving for a specific variable in a formula. 
  • Students may need review on graphing and relating the vertical and horizontal axes to real life problem solving.

 

Instructional Tasks

Instructional Task 1 (MTR.5.1) 
  • The Newz U Can Use company designs new video reels to help older adults learn how to use their cell phones and other devices. Using a graphing calculator, graph the following profit equation for Newz U Can Use: 
    P = −300p2 + 22,500p − 345,000. 
    • Part A. Determine the maximum profit for the profit equation. 
    • Part B. What will be the price point at the maximum profit? 

Instructional Task 2 (MTR.4.1, MTR.7.1)
  • Part A. Create a spreadsheet for a startup company that includes one month of income revenue from at least two sources, with a minimum of five costs/expenses. 
  • Part B. Calculate the end balance to determine a profit or loss for the startup company at months end. 
  • Part C. What information would you need to determine how to maximize the profit? 

Instructional Task 3(MTR.4.1) 
  • A company’s revenue and expense functions are shown. 
    R =−250p2 + 17,500p  E = −850p + 150,000 
    • Part A. Discuss with a partner why the expense, E, decreases as the price, p, increases. Create a scenario to justify your reasoning.
    • Part B. Determine the profit function for the company. 
    • Part C. Determine a price that maximizes the profit.

 

Instructional Items

Instructional Item 1 
  • Wrangler Ranch located in central Florida manufactures treats for livestock for sale at a local market. The expense equation for q bags of treats is E = 5.25q + 20,000. What is the cost per bag average for producing 500 bags to the nearest cent?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 - 2024, 2024 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 - 2024, 2024 and beyond (current))
7912120: Access Mathematics for Data and Financial Literacy (Specifically in versions: 2022 - 2023, 2023 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.FL.2.AP.2: Calculate the profit when given the expenses and revenue from a real-world problem.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plan

Marketing Mix: Price Setting:

Using the case study, "Colossal Cookie Profit Dilemma," students will identify pricing objectives for Ella’s business and they will discuss various factors business owners must consider when setting prices for the products. Students will select one of the pricing strategies and calculate the price for one of Ella’s cookies.

Type: Lesson Plan

Student Resources

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