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. Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 4 profit P = R – E maximum profit Key Terms

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 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

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 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

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 Must maximum profit occur at the same price as the maximum revenue? CHECK YOUR UNDERSTANDING

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit and state the maximum profit at this price.