financial algebra © 2011 cengage learning. all rights reserved. slide 1 2-7 the profit equation...
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 11
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
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 22
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 33
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 44
profitP = R – E
maximum profit
Key Terms
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 55
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 66
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 77
Example 1Example 1
Determine the profit equation for the Picasso Paints product in Lesson 2-5. The revenue and expense functions were
R = –500p2 + 30,000pE = –3,500p + 238,000
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 88
Example 2Example 2
Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit?
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 99
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 3EXAMPLE 3
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 1010
Must maximum profit occur at the same price as the maximum revenue?
CHECK YOUR UNDERSTANDING
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Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 1111
EXAMPLE 4EXAMPLE 4
Algebraically, determine the price of the Picasso Paints product that yields the maximum profit and state the maximum profit at this price.