2-7 THE PROFIT EQUATION OBJECTIVES Determine a profit equation given the expense and revenue equations. Determine the maximum profit and the price at which that maximum is attained. Slide 1 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-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 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Key Terms profit - money a company makes after expenses have been deducted from revenue maximum profit - greatest difference between revenue and expense Slide 3 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies http://my.hrw.com/math06_07/nsmedia/ tools/Graph_Calculator/graphCalc.html Slide 4 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. P = R – E where P is profit, R is revenue, and E is expenses Slide 5 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Example 1 Determine the profit equation for the Picasso Paints product in Lesson 2-5. The revenue and expense functions were R = –500p2 + 30,000p E = –3,500p + 238,000 Slide 6 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. CHECK YOUR UNDERSTANDING Suppose that the revenue and expense functions are R = –350p2 + 18,000p and E = –1,500p + 199,000. Write the profit equation. Slide 7 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Example 2 Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit? Slide 8 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. CHECK YOUR UNDERSTANDING Sketch the graph. Identify the points where zero profit is made. Explain your reasoning. Slide 9 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. EXAMPLE 3 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. Slide 10 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. CHECK YOUR UNDERSTANDING Must maximum profit occur at the same price as the maximum revenue? Slide 11 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit. Slide 12 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. CHECK YOUR UNDERSTANDING Use the profit function from Example 1 Check Your Understanding. Determine the price to the nearest cent that yields the maximum profit. Slide 13 Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Applications Pages 101 – 102, #2 – 16 even Slide 14 Financial Algebra © 2011 Cengage Learning. All Rights Reserved.