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We consider a real-time system that requires the time stimuli to the system are processed through sequences of tasks to be within specified upper bounds, where the set of tasks can be the mixture of preemptive and non-preemptive tasks, and we propose an algorithm to design a static priority scheduling for the system. In the algorithm, local search is used to determine priorities of tasks, and whenever the priorities are fixed, the periods of tasks are determined. This subproblem can be described as a mathematical programming formulation and is solved via linear programming techniques. Finally, we report computational results for sample instances from a company.