Consider a perishable product whose daily demand can range from a low of $51$ to a

high of $80.$ Demand is uniformly distributed over this range, so that sales of the product are

equally likely to be anywhere from $51$ to $80.$ Unsold units at the end of the day must be

discarded.

a$)$ The retailer selling the product wishes to maintain an $85\%$ service level $($i$.$e$.,$ probability of

fulfilling demand should be at least $0\mathrm{.}85).$ How many units should the retailer order each day?

b$)$ What is the minimum number of additional units that the retailer should order each day if the

desired service level is increased to $95\%?$