A large hospital uses a certain intravenous solution that it maintains in inventory. Assume the hospital uses reorder point method to control the inventory of this item. Assume the hospital operates $52$ weeks per year. Pertinent data about this item are as follows:

Forecast of demand ${?}^a=1,000$ units per week

Forecast error ${?}^a,$ std$.$ dev. $=50$ units per week

Lead time $=4$ weeks

Carrying cost $=25\%$ per year

Purchase price, delivered $=$$$52$ per unit

Replenishment order cost $=$$$20$ per order

Stockout cost $=$$$10$ per unit

In$-$stock Probability during the lead time $=90\%$

${?}^{\text{a}\text{N}\text{o}\text{r}\text{m}\text{a}\text{l}\text{l}\text{y}\text{d}\text{i}\text{s}\text{t}\text{r}\text{i}\text{b}\text{u}\text{t}\text{e}\text{d}}$

Due to possible rounding effect, please pick the closest number in the following options.

If the hospital orders $800$ units each time, what's the annual stock$-$out cost?

$624$

$6240$