This paper considers an unreliable manufacturing system with random processing times and random product demands. The system can produce many part types and its total capacity is constrained by a fixed constant. The objective is to find an optimal service-rate allocation policy between different part types by minimizing the expected discounted inventory and backlog cost. Structural properties of the optimal control policy are investigated, It is shown that the optimal policy is of a switching structure. For producing a one part type case, the optimal control is a threshold policy. For producing a two part types case, the optimal control can be described by three monotone switching curves and its asymptote properties are derived. Numeric examples are given to illustrate the results.