Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of $305$ per day, and it uses these subcomponents at a rate of $12,600$ per year $($of $250$ working days$).$ Holding costs are $$2$ per item per year, and ordering costs are $$31$ per order.

a$)$ What is the economic production quantity? $684\mathrm{.}05$ units $($round your response to two decimal places$).$

b$)$ How many production runs per year will be made? $18\mathrm{.}41$ production runs $($round your response to two decimal places$).$

c$)$ What will be the maximum inventory level? units $($round your response to two decimal places$).$