We consider a class of discrete-event systems (DES) that involves the control of resources allocated to tasks under real-time constraints. This is motivated by power-limited wireless environments such as sensor networks, where the objective is,to minimize energy consumption while guaranteeing that task deadlines are always met. In obtaining optimal offline controllers for such systems, we prove that simple static control gives the unique optimal solution. The result is of interest because it asserts the optimality of a simple controller that does not require any data collection or processing in environments where the cost of such actions is high.