We address the problem of scheduling customers in a multiclass G/G/1 queue so as to minimize a weighted sum of the workloads of the different classes. We establish that the nonidling, preemptive, fixed prority policy that schedules customers belonging to the class having the maximum weight minimizes the cost function pathwise at any point in time. This result is based on the application of elementary forward induction arguments and is shown to hold for a very general class of policies. A new proof for the optimality of the c-rule in the multiclass G/M/1 queue is then obtained as an easy corollary of the first result.