The sales manager, Julie, conducted a market survey with the following results for number of Bouncy Balls sold, x, based upon the selling price, p. x (thousand balls) P $$ 37.5 1.25 196.5 0.95 4) Graph the Revenue Function. 355.5 0.65 Revenue 1) A demand function is a function that describes the relationship between number of items sold and selling price. Determine the demand function for the relationship between number of Bouncy Balls sold and selling price. In this case, the relationship is linear. Solve the equation for p. Total Revenue 567.5 0.25 p= 2) Revenue is defined as the total sales of a product. A revenue function may be found by multiplying the number of items sold by the individual selling price. Use the equation found in 1) to determine the revenue function. R(x)=xp R(x) = 3) Use the revenue function to complete the table of values below. 37.5 196.5 355.5 x (thousand balls) R(x) $$ 567.5 Maximizing Revenue & Minimizing Costs 5) 6) 7) What quantity of Bouncy Balls will yield the maximum revenue? What is the maximum revenue? What price should the company charge in order to maximize the revenue? Minimizing Costs George, the production supervisor, has provided the following cost function for the same type of Bouncy Ball. Cost: C(x) = 0.0002x -0.13x + 55 when x thousand Bouncy Balls are produced. 8) Use the cost function to complete the table of values below. x (thousand balls) 37.5 196.5 C(x) (thousands $$) 9) Graph the Cost Function. Page 2 of 3 355.5 567.5 10) What quantity of Bouncy Balls will yield the minimum costs? 11) What is the minimum cost? Recall that the profit can be found by finding the difference between revenues and costs. 12) Find the Profit function, P = R-C. P(x) =_ 13) Use the profit function to complete the table of values below. x (thousand balls) 37.5 196.5 P(x) (thousands $$) 14) Graph the Profit Function. 15) Find the maximum possible profit. Total Profit 355.5 567.5 Number of Bouncy Balls 16) How many Bouncy Balls must be produced and sold in order to earn the maximum profit?