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$$ day, and it uses these subcomponents at a rate of $12,100$ per year$($of $250$ working$$ days$).$ Holding costs are $$$$3$ per item per$$ year, and ordering costs are $$$$29$ per order.

$$a$)$ What is the economic production$$ quantity? $\_\_\_$ units $($round your response to two decimal$$ places$).$

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

$$c$)$ What will be the maximum inventory$$ level?

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

$$e$)$ What is the annual cost of ordering and holding$$ inventory?