A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars).

(a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.

Advertising …………..…………………….. Total Revenue

20 …………………………………………………… $6101

22 …………………………………………………… $6350

25 …………………………………………………… $6378

27 …………………………………………………… $6453

28 …………………………………………………… $6423

29 …………………………………………………… $6360

31 …………………………………………………… $6231

(b) The quadratic function of best fit to these data is

R(A) = -7.76A² + 411.88A + 942.72

Use this function to determine the optimal level of advertising.

(c) Use the function to predict the total revenue when the optimal level of advertising is spent.

(d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit.

(e) Use a graphing utility to draw a scatter diagram of the data and then graph the quadratic function of best fit on the scatter diagram.