Advertising andproduction of a seasonal good for a heterogeneous market

We bring some concepts from market segmentation, which is a fundamental topic of marketing theory and practice, into the statement of an advertising and production problem for a seasonal product with Nerlove- Arrow's linear goodwill dynamics. We consider two kinds of situations. In the rst one the advertising process can reach selectively each segment. In the second one one advertising medium is available which has a known eectiveness spectrum for a non-trivial set of segments. In both cases we solve, using the Pontryagin's Maximum Principle conditions, the optimal control problems in which goodwill productivity of advertising is concave and good production cost is convex. Two special cases are discussed in detail.