Applying the maximum principle to the advertising expenses control

The article contains the dynamic, continuous model of the optimal advertising expenses control, taking into account the influence of time-lags of the consumers' reaction on advertising impact and on the previous purchases. The paper tries to solve the problem of maximizing the total profit of a company during the planning period under the restriction, reflecting the target audience reaction. In this case the initial problem is formulated as a system of equations of Volterra type.