Problem $3$

The daily demand for Ironcoat paint at the Top Value Hardware Store in North Bay is normally distributed, with a mean of $30$ litres and a standard deviation of $10$ litres. The holding cost is $$0\mathrm{.}15/$litres$/$year$.$ The lead time for receiving an order of paint from the paint distributor is eight days. Since this is the only paint store in North Bay, the manager currently maintains only a $75\%$ service level. The manager subsequently learned that a new paint store would open soon in North Bay, which has prompted her to increase the service level to $85\%.$ How much will safety stock increase in order to provide the higher service level? $($hint: if you are solving the problem in days instead of year, then marks$)$