This paper demonstrates the use of model checking to solve the problem of optimal task scheduling in a flexible manufacturing system. The system is modelled as a discrete event system, for which the least restrictive safe behaviour is synthesised according to supervisory control theory. Then timing constraints are added to the model in the form of extended finite-state machines, and time-optimal schedules are computed using the discrete event systems and model checking tool Supremica. In the case study considered in this paper, which previously was only solved heuristically, the method successfully produces optimal schedules to manufacture up to 30 products of two different types. The method is furthermore used to find an optimal cycle, solving the scheduling problem of the case study for an arbitrary number of products in optimal or asymptotically close to optimal time.