$12\mathrm{.}18$ Race One Motors is an Indonesian car manufacturer. At its largest manufacturing facility, in Jakarta, the company produces subcomponents at a rate of $300$ per day, and it uses these subcomponents at a rate of $12,500$ per year $($of $250$ working days$).$ Holding costs are $$2$ per item per year, and ordering $($setup$)$ costs are $$30$ per order. a$)$ What is the economic production quantity? b$)$ How many production runs per year will be made? c$)$ What will be the maximum inventory level? d$)$ What percentage of time will the facility be producing components? e$)$ What is the annual cost of ordering and holding inventory?"