Daily demand for aspirin at Shoppers Pharmacy is normally distributed, with a mean of $40$ bottles and a standard deviation of $5.$ The replenishment lead time from the supplier is two days. The current inventory policy at Shoppers is to order $200$ bottles when the quantity on hand drops below $45.$ Each bottle costs Shoppers $$4,$ and the pharmacy uses an annual holding cost of $20$ percent.

a$.$ If all unfilled demand is assumed to be backlogged and carried over to the next cycle, what cost of understocking justifies the current policy?

b$.$ If all unfilled demand is assumed to be lost, what cost of stocking out justifies the current policy?

c$.$ Shoppers believes that all unfilled demand can be backlogged if customers are given a $$1\mathrm{.}50$ discount on their next purchase $($effectively making the cost of understocking $$1\mathrm{.}50).$ What inventory policy $($CSL$,$ ROP and SS$)$ do you recommend for Raxel?