This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an earliest due date first algorithm provides an optimal nonpreemptive schedule for unit execution time tasks, then the preemptive priority scheduling algorithm, referred to as smallest laxity first, provides an optimal preemptive schedule for real-execution-time tasks. When the objective is to minimize the makespan, we get the same kind of result between highest level first schedules solving nonpremptive tasks with unit execution time and the longest remaining path first schedule for the corresponding preemptive scheduling problem with real-execution-time tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained.