Question:Home Depotsells the LawnBoy T750 lawn mowers at 81 stores in the Western US.Weekly demand for the T750 at each of the stores is identical and given by:X_~Normal (50, 30).Assume that the demands at the 81 stores areindependentof each other.The manufacturer's lead time for supplying the mowers is 9 weeks.Home Depot has a stated policy of 96% cycle service level for mowers.

a.How much safety stock is requiredat each store?

b.The chain is considering centralizing the inventory of the T750 to a distribution center that will serve all 81 stores.How much safety stock would be requiredat the DCto provide the same cycle service level of 96%?

c.If the cost of each mower is $600, andHome Depotuses a 25% holding cost rate, what is the annual savings for the chain in inventory holding costs as a result of the centralization?