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Maximizing Profit Equation: Analysis & Examples

Learn how to determine profit equation from revenue and expense functions and find maximum profit attained. Explore graphing methods to visualize profit equations and interpret zero-profit points. Algebraically solve for the price yielding maximum profit.

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Maximizing Profit Equation: Analysis & Examples

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  1. 2-7THE PROFIT EQUATION OBJECTIVES Determinea profit equation given the expense and revenue equations. Determinethe maximum profit and the price at which that maximum is attained.

  2. profit P = R – E maximum profit Key Terms

  3. 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

  4. Example 2 Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit?

  5. 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.

  6. CHECK YOUR UNDERSTANDING Must maximum profit occur at the same price as the maximum revenue?

  7. EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit and state the maximum profit at this price.

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