Demand for a popular hospital bed from a Hill$-$Rom warehouse in the US is normally distributed with a mean of $402$ units$/$week and standard deviation of $60$ units$/$week$.$ Lately, Hill$-$Rom's contract manufacturer has been unreliable with its deliveries. Hill$-$Rom estimates the lead time is normally distributed with a mean of $6$ weeks and standard deviation $4$ weeks. Hill$-$Rom orders the beds at a unit cost of $$2,167.$ The annual cost of carrying inventory at the warehouseis $31\%$ of the purchase cost per unit per year. Hill$-$Rom reviews its inventory continuously. Assume the warehouse operates $52$ weeks$/$year$,7$ days$/$week$,$ and $364$ days$/$year$.$

Suppose that Hill$-$Rom works with its contract manufacturer to improve reliability in the supply chain such that lead times are guaranteed at $6$ weeks.

Compute the savings in annual holding cost of the safety stock $($in $$)$ needed to maintain a service level of $92\%.$

Carry calculations to at least $3$ decimal places.

Round your answer to the nearest tenth of a dollar $($one decimal place$).$