A single season production and advertising control problem with bounded final goodwill

We consider the problem of a firm which seeks the maximum profit from the offer of a seasonal product on the market and has to reach a fixed goodwill value at the end of the season. Production and sale of the product take place in two disjoint and consecutive subintervals of each season and the firm can advertise the product at every time of the season. For the original optimal control problem we present a new formulation in the framework of nonlinear programming, depending on the solution of three simpler optimal control problems. We analize the characteristics of the solutions of the nonlinear programming problem.