Textbook Problem

The General Flakes Company sells a brand of lo-fat breakfast cereal that appeals to people of all age groups and both genders. The company advertises this cereal in a variety of 30-second television ads, and these ads can be placed in a variety of television shows. The ads in different shoes vary by cost —some 30-second slots are much more expensive than others—and by the types of viewers they are likely to reach. The company has segmented the potential views into six mutually exclusive categories: males age 18 to 35; males age 36 to 55; males over 55; females age 18 to 35; females age 36 to 55; and females over 55. A rating service can supply data on the numbers of viewers in each of these categories who will watch a 30-second ad any particular television show. Each such viewer is called an exposure. The company has determined the required number of exposes it wants to obtain these required exposures at minimum cost. The data on costs per ad, numbers of exposures per ad, and minimal required exposures are listed in Table 4.1, where numbers of exposures are expressed in millions, and costs are in thousands of dollars. What should the company do?

Suppose there are three objectives, not just two: the total advertising cost, the total number of excess exposures to men, and the total number of excess exposures to women. Continuing the approach suggested in the previous problem, how might you proceed? Take it as far as you can, including a sensitivity analysis and a trade-off curve.