the stock$-$out cost is replace with a Type I service objective of $95$ percent. Find the optimal values of $($Q$,$ R$)$ in this case.

$3.$

Suppose that in Problem $3$ a Type II service objective of $95$ percent is substituted for the stock$-$out cost of $$12\mathrm{.}80.$ Find the resulting values of Q and R$.$

The monthly demand for the filter follows a normal distribution with mean $280$ and standard deviation $77.$ Order lead time is assumed to be five months. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back$-$ordered, and the cost assessed for each back$-$ordered demand is $$12\mathrm{.}90.$ Determine the following quantities:

a$.$

The optimal values of the order quantity and the reorder level.

b$.$

The average annual cost of holding, setup, and stock$-$out associated with this item assuming that an optimal policy is used.

c$.$

Evaluate the cost of uncertainty for this process. That is$,$ compare the average annual cost you obtained in part $($b$)$ with the average annual cost that would be incurred if the lead time demand had zero variance.

$2.$

Suppose that in Problem $3$ the stock$-$out cost is replace with a Type I service objective of $95$ percent. Find the optimal values of $($Q$,$ R$)$ in this case.

$3.$

Suppose that in Problem $3$ a Type II service objective of $95$ percent is substituted for the stock$-$out cost of $$12\mathrm{.}80.$ Find the resulting values of Q and R$.$