Production control model with a lead time for items with multi-period lifetime

We consider a production management problem for items with a multi-period lifetime. An item needs one period for its production, does not deteriorate while it is alive and therefore is sold at the same selling price. We want to obtain the amount of production maximizing the expected total net profit. We formulate this model by dynamic programming, derive the equation from which the optimal production policy can be obtained and give the concrete solution in the case of exponential demand.