Starting with the solution to the advertising selection problem in Example 7.6, suppose the company, for whatever reason, cannot place ads on “Sports Center.” Make the appropriate changes in the model and rerun Solver. Comment on the changes to the changing cells. Then comment on the change to the total cost. In particular, explain how the total cost can change so much in the direction it changes.
EXAMPLE 7.6 ADVERTISING SELECTION WITH NONLINEAR RESPONSE FUNCTIONS
I n this example, we revisit the problem faced by the General Flakes Company in Example 4.1 of Chapter 4. The company must decide how many ads to place on each of several television shows to meet exposure constraints for each of six groups of customers. (Refer to Figure 7.26 and the file Advertising Selection.xlsx for the specific inputs.) The difference now is that each combination of television show and customer group has its own advertising response function of the form in Equation (7.4). That is, there are constants a and b of the response function for each such combination. (These constants appear in rows 5 to 10 and 14 to 19 of the file.) The company wants to find the selection of ads that minimizes its total cost of meeting all exposure requirements.
Objective To use a nonlinear model to find a minimum-cost way of meeting all exposure requirements.
WHERE DO THE NUMBERS COME FROM?
We already discussed where many of the inputs come from in Example 4.1 of Chapter 4. The new inputs, the parameters of the various response functions, come from fitting response functions, exactly as in the previous example, for each combination of television show and customer group. Of course, this assumes the company has enough historical data to carry out this procedure. The numbers used here are for illustration only, although they are reasonable.