1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 2-7 THE PROFIT EQUATION Determine a profit equation given the expense and revenue equations. Determine the maximum profit and the price at which that maximum is attained. OBJECTIVES

2. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Create an equation based on the following: A company has fixe costs of $30, 000 and variable costs of $2 per widget. Express the expenses E as a function of x. Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 profit - money a company makes after expenses have been deducted from revenue maximum profit - greatest difference between revenue and expense Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies Slide 4 http://my.hrw.com/math06_07/nsmedia/ tools/Graph_Calculator/graphCalc.html http://my.hrw.com/math06_07/nsmedia/ tools/Graph_Calculator/graphCalc.html

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 P = R – E where P is profit, R is revenue, and E is expenses

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 Example 1 Determine the profit equation for the Picasso Paints product in Lesson 2-5. The revenue and expense functions were R = –500 p 2 + 30,000 p E = –3,500 p + 238,000

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 Suppose that the revenue and expense functions are R = –350 p 2 + 18,000 p and E = –1,500 p + 199,000. Write the profit equation. CHECK YOUR UNDERSTANDING

8. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 Example 2 Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit?

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 Sketch the graph. Identify the points where zero profit is made. Explain your reasoning. CHECK YOUR UNDERSTANDING

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 Graph the revenue, expense, and profit functions on the same coordinate plane. Interpret the zero-profit points, the maximum profit, and how the functions relate to each other. EXAMPLE 3

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 Must maximum profit occur at the same price as the maximum revenue? CHECK YOUR UNDERSTANDING

12. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 12 EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit.

13. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 13 Use the profit function from Example 1 Check Your Understanding. Determine the price to the nearest cent that yields the maximum profit. CHECK YOUR UNDERSTANDING

14. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. ApplicationsApplications Pages 101 – 102, #2 – 16 even Slide 14