The paper deals with the problem of scheduling jobs on a processor which can simultaneously process all the jobs, and where the job processing intensity is a continuous function of an instantaneous resource usage. A server can control the processing time of jobs through the allocation of an available resource in time. The first problem considered is to minimize the weighted flow time, provided that all the jobs are ready for processing at the same point in time. The second problem is to minimize the completion time of all the jobs, provided that job release dates are different and known. These problems are formulated as optimal control problems. It is shown that for each of them there exists a class of jobs for which sequencing the jobs in a certain preference order and processing each job with maximum intensity yields an optimal schedule.