This paper presents the analysis of the optimal production and corrective maintenance planning problem for a failure prone manufacturing system consisting of several machines in tandem. These machines are subject to breakdowns and repairs and the control problem is subject to non-negative constraints on work-in-processes (WIP). The introduction of the corrective maintenance will increase the availability of the production system which guarantees the improvement of the system's productivity if the planning production is well done. The system capacity is assumed to be described by a finite state Markov chain which depends on the corrective maintenance policy. The decision variables are the production and the machine repair rates which influence the WIP levels, the surplus level and the system capacity respectively. The objective of the problem is to minimize the cost of intermediate storages, surplus and repair activities. A computational algorithm, based on numerical methods, is given for solving the optimal control problem. Finally, a numerical example of a two-machine flowshop is presented to illustrate the usefulness of the proposed approach.