FairPrice Xtra in Jurong Point is using a fixed period inventory system to control its inventory of brown sugar ice cream from Taiwan. The average monthly demand for brown sugar ice cream is $1,000$ tubes and the following information is available:

$$ Lead time $=1$ month

$$ Ordering cost $=$ $$150$ per order

$$ Unit price $=$ $$10$

$$ Carrying$/$holding rate $=20\%$

$$ Standard deviation of monthly demand $=80.$

$$ Assume $4$ weeks

Analyse the review period and optimal replenishment level with safety stock. Comment on how the system should be managed.