The Profit Equation Unit 2.7 10/23/17

Key Terms profit maximum profit

How do revenue and expenses contribute to profit calculation? What are the names of different companies that produce the same product? What aspects of the production might not be identical among the companies? If there is only one breakeven point, what does it mean for production and sales?

How do revenue and expenses contribute to profit calculation? Maximum Profit P = R – E Profit = Revenue – Expenses Greatest difference b/t Revenue & Expenses

Example 1 R = –500p2 + 30,000p E = –3,500p + 238,000 P = R – E 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 P = R – E P = -500p2 + 30,000p –(-3,500p + 238,000) = -500p2 + 30,000p + 3,500p – 238,000 = -500p2 + 33,500p – 238,000

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. P = R – E = -350p2 + 18,000p – (-1,500p + 199,000) = -350p2 + 18,000p + 1,500p – 199,000 = -350p2 + 19,500p – 199,000

Find 3 points of a parabola Example 2 Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit? Find 3 points of a parabola If p = 0 what does Profit =? Axis of Symmetry = b/-2a Double the AOS to find the 2nd point on the x-axis Find Vertex by plugging AOS into function

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

EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit.

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.