The following control problem in manufacturing is addressed. Jobs of two priority classes, C1 and C2, arrive at a system with two nonidentical machines. Class C1 jobs with higher priority have dispatch preference over C2 jobs with lower priority. The problem is to dispatch appropriate fractions of class C1 jobs to machines 1 and 2 so that the average flow time of C1 jobs is minimized and neither C1 jobs nor C2 jobs are lost. The analytical solution to the problem is derived for various system disciplines, including 1) nonpreemptive priorities, 2) preemptive priorities with resumption, 3) preemptive priorities with resumption and setup, and 4) nonpreemptive priorities with multiple vacations.