The demand for a certain product has shown to be relatively stable; its sales are not subject to any seasonal influence, and demand is not expected to change in the future. In fact, during the last $10$ lead times, the following demand was observed: $64514832932147574146$ Assuming that this demand is a good representative of total demands in future lead times and a reorder point of $51$ is used, compute: a$.$ The various possible shortage sizes and their probabilities of occurrence $($HINT: Assume that these are the only values that the demand can take, each with a $0\mathrm{.}1$ probability of occurring$).$ b$.$ The expected $($or average$)$ shortage. c$.$ What reorder point would you use if the average shortage was to be no larger than $5$ units? What is the associated probability of a stockout?The demand for a certain product has shown to be relatively stable; its sales are not subject to any seasonal influence, and demand is not expected to change in the future. In fact, during the last $10$ lead times, the following demand was observed: $64514832932147574146$ Assuming that this demand is a good representative of total demands in future lead times and a reorder point of $51$ is used, compute: a$.$ The various possible shortage sizes and their probabilities of occurrence $($HINT: Assume that these are the only values that the demand can take, each with a $0\mathrm{.}1$ probability of occurring$).$ b$.$ The expected $($or average$)$ shortage. c$.$ What reorder point would you use if the average shortage was to be no larger than $5$ units? What is the associated probability of a stockout?