On an Optimal Advertising Model with Lagged effect of Advertising

This paper deals with a modification of the Vidale-Wolfe advertising model. The model is enriched by an assumption that the current intensity of sales depends mainly on the past intensity of advertising. Mathematical formulation results in a system of two ordinary differential equations. First we study special case when the intensity of advertising is constant. Then we concentrate on finding an optimal strategy of advertising with regard to a given cost function. For this purpose we use the Pontryagin maximum principle.