Demand for a leather tote bag at Leatherology is constant at $6,723$ units per year. Leatherology purchases the bags from its supplier for a cost of $$55$ per unit. The lead time to receive an order from the supplier is $5$ days. Leatherology incurs a fixed order cost of $$2,462$ each time it places an order regardless of the number of units ordered. The holding cost per unit per year is $20\%$ of the per unit purchase cost. Leatherology currently orders $442$ units each time it places an order. Assume the firm operates $7$ days per week, $52$ weeks per year, and $364$ days per year.

Calculate the optimal order quantity.

Carry your calculations to at least $3$ decimal places.

Enter your answer rounded to one decimal place $($nearest tenth$).$