A large retailer reviews its inventory for a popular product periodically every six days. The demand for this product is Normally distributed: mean daily demand is 28.6 and standard deviation of daily demand is 8.81. Following an order, it takes 3 days for the supplier to replenish the retailers inventory.

a. What would be the base stock to achieve a target instock probability of 99.2%?

b. If S = 289, answer questions b. i and b.ii

i. What is the expected backorder?

ii. What is the expected on-order inventory?