Central Hospital Supply has a policy that a hospital can expect its orders to be filled directly from stock 92 percent of the time. If any one item on an order is out of stock, the entire order will be held as a back order to avoid additional shipping costs. Orders typically include up to ten items. A sampling of the orders over the last year shows that six combinations of products frequently appear on orders, as follows:

Inventory levels have been set so that products A, B, C, D, E, and F have a common service level of 0.95 each. The remaining products are set at 0.90 each.
a. Is the firm meeting its inventory service target?
b. If not, at what item service levels would these two groups of products have to be set to meet the 92 percent order fill rate?

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Combination A.CEG Order Itenm Frequency of Order 0.20 015 0.05 A,B.C.D.FH.5- 0.15 D.F.G.H.AJ 0.30 0.15 1.00 A.C.D.E