Determining optimal production and advertising policies for a seasonal product

We study a nonlinear programming problem whose objective function represents the profit a firm obtains from producing and selling a seasonal product, allowing for production, inventory, advertising and unsold stock costs. We observe that the problem is nondifferentiable and has an optimal solution, possibly not unique. We sketch an algorithm to determine the solutions of the problem, exploiting the knowledge of a special continuous curve in the feasible set, to which the original problem can be restricted.