Race One Motors is an Indonesian car manufacturer. At its largest manufacturing$$ facility, in$$ Jakarta, the company produces subcomponents at a rate of $290$ per$$ day, and it uses these subcomponents at a rate of $12,500$ per year$($of $250$ working$$ days$).$ Holding costs are $$$$3$ per item per$$ year, and ordering costs are $$$$32$ per order.

$$a$)$ What is the economic production$$ quantity? $567\mathrm{.}65$ units $$

$$b$)$ How many production runs per year will be$$ made? $22$

$$c$)$ What will be the maximum inventory$$ level? $469\mathrm{.}78$

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$$d$)$ What percentage of time will the facility be producing$$ components?

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$($enter your response as a percentage rounded to two decimal$$ places$).$