# a. For each of the three advertising media, draw a graph of the number of sales versus

## Question:

a. For each of the three advertising media, draw a graph of the number of sales versus the number of advertisements by plotting the sales for the five points provided by Sid Jackowitz and then drawing a smooth curve through (or very near) these points. (Fractional advertisements are allowed by using only a portion of the available outlets.)

b. For each of the advertising media, use Excel's curve fitting method to (1) obtain a nonlinear formula for the sales graph and then (2) construct the graph. In each case, try three Excel options for the form of the graph-a polynomial of order 2 (the quadratic form), a polynomial of order 3, and the logarithmic form-and then choose the option that you feel provides the best fit.

c. Using your results from part b, write an expression for the total profit (as defined by Claire) in terms of the number of advertisements of each type.

d. Using your result from part c, revise the spreadsheet model in Figure 3.7 (available on the CD-ROM) so that it maximizes total profit instead of the total number of exposures, and then solve.

e. Use the sales tables provided by Sid Jackowitz to apply separable programming to this problem when maximizing total profit.

f. Compare your results in parts d and e with those in Figure 3.7 and then give your recommendation (with a brief explanation) for the best advertising mix. Do you feel it was worthwhile to introduce a nonlinear profit function into the model in order to refine the linear programming model used in Figure 3.7?

FIGURE 3.3

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