Modelling smoothly the joint effect of several advertising media on sales in a homogeneous market

Decision on the use of different advertising media is a critical issue in marketing. Drawing on some literature related to the dynamic Nerlove-Arrow model, we propose a nonlinear programming framework for discussing how different advertising media may jointly affect the demand for a good. Starting from the idea that different advertising efforts may not simply add (linearly) to produce the demand result, we examine a few special media combination mechanisms which can be represented by smooth functions.