In this study, we consider a stochastic inventory system in which the objective of the manufacturer is to maximize the long-run average profit by dynamically offering the selling price and switching the production on or off. The demand process is non-homogeneous Poisson with a price-dependent arrival rate. System costs consist of switching costs, inventory holding and backlogging costs. We show that an (s, S, p) policy is optimal. Moreover, we characterize the structural properties of the optimal profit function and pricing strategy, and show that the optimal price is a quasiconcave function of the inventory level when the production is off and is a quasiconvex function when the production is on.