Advertising decisions for a segmented market

We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments variably and we assume that the advertising effects on demand over time are mediated by a vector goodwill variable. A first general advertising decision problem is stated and solved in the non-linear programming framework. A preference index is then obtained for the medium selection problem when each segment demand function is linear in goodwill and each medium advertising cost function is quadratic in its level. Finally the theoretical case of disjoint advertising media is discussed