Home Depot sells 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...

Home Depot sells 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 are independent of 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 required at 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 required at the DC to provide the same cycle service level of 96%?

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