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.