A manufacturing plant has an annual demand of $10,000$ units for a component. The setup cost for a production run is \50$, and the annual holding cost is$$4$per unit. According to the Economic Production Quantity model, the optimal batch size is$Q = \sqrt{\frac{2 D S}{H}}$, where$D$is annual demand,$S$is setup cost, and$H$ is holding cost. What is the optimal batch size?