$2-,$ The Ziggys Bicycle Shop operates $364$ days a year, closing only on Christmas Day.

The shop pays $$400$ for a particular bicycle purchased from the manufacturer. The

annual holding cost per bicycle is estimated to be $20\%$ of the dollar value of inventory.

The shop sells an average of $20$ bikes per week. The cost for each order is $$225.$

Determine the optimal order quantity. $($Round to two decimal places$).$