The purchase lead time is approximately $15$ days. For simplicity, suppose that there are only two types of Energizer batteries in the warehouse: Item #$0378422$CA$,6$V Lantern battery with annual demand of $5,767$ units and price of $$3\mathrm{.}85$ each, and Item #$0378539$CA$,6$V Lantern battery with annual demand of $603$ units and price of $$7\mathrm{.}54$ each. a$.$ Suppose that the fixed cost of a purchase order for one SKU is $$3\mathrm{.}50$ and the variable cost of each additional line item $($SKU$)$ is $$0\mathrm{.}50.$ Also suppose that holding cost rate is $20$ percent of unit cost per year. Determine the optimal order interval. B$.$ The forecast demand for Item #$0378422$CA is $138$ units per week for the next few weeks and the standard deviation of demand is estimated to be $37$ units per week. Currently there are $555$ units on hand in the warehouse and none are on order. The service level for this SKU is desired to be $98\mathrm{.}5$ percent. Calculate the Imax $($order up to level$)$ for this battery, and determine the quantity to order.