1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 2-6 BREAKEVEN ANALYSIS Determine the breakeven prices and amounts using technology or algebra. OBJECTIVES

2. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Graph each on the same set of axes. y = x 2 and y = -2x Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 zero net difference - difference between expense and revenue equals zero quadratic formula - Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies Slide 4

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 Example 1 Determine the prices at the breakeven points for the Picasso Paints product in Lesson 2-5. The expense function is E = –3,500 p + 238,000, and the revenue function is R = –500 p 2 + 30,000 p.

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 The expense function for a particular product is E = –2,000 p + 125,000. The revenue function for that product is R = –600 p 2 + 18,000 p. Determine the prices at the breakeven points for this product both algebraically and graphically. CHECK YOUR UNDERSTANDING

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 Knowing that the two breakeven prices have been rounded to the nearest cent, what would you expect when each is substituted into the expense and revenue equations? EXTEND YOUR UNDERSTANDING

8. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 Example 2 Determine the revenue and expense for the Picasso Paints product at the breakeven points found in Example 1.

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 How could you have improved on the error when calculating the expense and revenue values? CHECK YOUR UNDERSTANDING

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 Use a spreadsheet to determine the breakeven price for the Picasso product. EXAMPLE 3

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 What cell formulas were used to identify the a, b, and c values shown in B11, B12, and B13? CHECK YOUR UNDERSTANDING

12. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. ApplicationsApplications Pages 95 – 96, #2 – 14 even Slide 12