Guitar Center $($GC$)$ purchases USB audio interface units from its supplier for a cost of $$281$ per unit. The lead time to receive an order from the supplier is $9$ days. Guitar Center incurs a fixed order cost of $$1,296$ each time it places an order regardless of the number of units ordered. Demand for the audio interface units at the warehouse is constant at $227$ units per week. The holding cost per unit per year at the DC is $35\%$ of the per unit purchase cost. Guitar Center currently orders $687$ units in each order. Assume Guitar Center operates $7$ days per week, $52$ weeks per year, and $364$ days per year.

Calculate the optimal total annual relevant cost in dollars.