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We consider a single-processor firm real-time (FRT) system with exponential interarrival and execution times for jobs with relative deadlines following a general distribution. The scheduling policy of the system is first-come first-served (FCFS) and the capacity of the system is arbitrary. This system is subject to an arbitrary-shaped time/utility function (TUF), which determines the accrued utility of each job according to its completion time. It is considered that the system power consumption at different working states is predetermined for each processor speed. We have proposed an exact analytical method for the calculation of specific performance and power-related measures of the system. The resulting analytical formulations for the performance measures are functions of the processor speed and system capacity. These measures are optimized through appropriate selections of the speed using derivatives and the capacity employing numerical search methods. Some experimental results are presented for different unimodal TUFs in systems with deterministic and exponential relative deadlines. For the latter distribution, the results are compared against similar results obtained through simulation for the nonpreemptive earliest-deadline-first (NP-EDF) scheduling policy. The comparisons show that FCFS is superior to NP-EDF for some measures and TUFs.