The Profit Equation Unit 2 7 102317 Key

The Profit Equation Unit 2. 7 10/23/17

Key Terms profit maximum profit Slide 2

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? Slide 3

How do revenue and expenses contribute to profit calculation? Profit P=R–E Profit = Revenue – Expenses Maximum Profit Greatest difference b/t Revenue & Expenses Slide 4

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Example 1 Determine the profit equation for the Picasso Paints product in Lesson 2 -5. The revenue and expense functions were R = – 500 p 2 + 30, 000 p E = – 3, 500 p + 238, 000 P=R–E P = -500 p 2 + 30, 000 p –(-3, 500 p + 238, 000) = -500 p 2 + 30, 000 p + 3, 500 p – 238, 000 = -500 p 2 + 33, 500 p – 238, 000 Slide 7

CHECK YOUR UNDERSTANDING Suppose that the revenue and expense functions are R = – 350 p 2 + 18, 000 p and E = – 1, 500 p + 199, 000. Write the profit equation. P=R–E = -350 p 2 + 18, 000 p – (-1, 500 p + 199, 000) = -350 p 2 + 18, 000 p + 1, 500 p – 199, 000 = -350 p 2 + 19, 500 p – 199, 000 Slide 8

Example 2 Use a graphing calculator to draw the graph of the profit equation from Example 1. What is the maximum profit? 1. Find 3 points of a parabola If p = 0 what does Profit =? 2. Axis of Symmetry = b/-2 a 3. Double the AOS to find the 2 nd point on the x-axis 4. Find Vertex by plugging AOS into function 1. Slide 9

CHECK YOUR UNDERSTANDING Must maximum profit occur at the same price as the maximum revenue? Slide 10

EXAMPLE 4 Algebraically, determine the price of the Picasso Paints product that yields the maximum profit. Slide 11

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 12