The annual demand for the Super Thrive brand plant food manufactured by Cumberbatch and Dunst Indoor Plants Company is $20,000$ pounds. The annual holding cost $($also known as carrying charge$)$ is $$0\mathrm{.}05$ per pound, and Operations Manager Kirsten Benedict has calculated the cost of every machine set$-$up for making the plant food to be $$20.$ What is the economic order quantity $($i$.$e$.,$ the optimal production batch size$)$ based on the information provided?