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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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profitP = R – E

maximum profit

Key Terms

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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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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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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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Must maximum profit occur at the same price as the maximum revenue?

CHECK YOUR UNDERSTANDING

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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.