HP Company supplies ink cartridges for printers on the aftermarket $($i$.$e$.$ they sell replacement cartridges$).$ The demand for the cartridge is $400$ units per week, with a standard deviation of demand of $33\mathrm{.}5$ units per day. The holding cost of the cartridge is $$5/$unit$/$year while the ordering cost is $$100/$order$.$ The company works for $50$ weeks per year at $5$ days per week. The desired service level for this part is $99\%,$ it takes $5$ days to get it from the supplier. The company is investigating the possibility of implementing a continuous review $($EOQ$)$ inventory system.

In the abve case, how much safety stock should be carried in the continuous review system described above $($rounded up to the nearest whole number$)?$ The z score from the normal distribution chart is $2\mathrm{.}33,$ for a $99\%$ service level.

Safety Stock $=$ Z x Sigma$($Lead Time$)$