This paper is concerned with scheduling of a marketing-production system in which the demand rate changes in accordance with marketing actions. Our goal is to provide illuminating descriptions and insight on the optimal control policies. A basic building-block model involving a single machine is developed. The objective is to choose the rates of production and marketing to maximize the overall profit, Consisting of a pair of hedging points, the optimal policy is attractive in practice because of its simplicity and can be computed by solving algebraic equations, Aiming at obtaining analytic solutions, various control regions of the optimal policy are depicted; the structure of the hedging-point policy is fully analyzed.