Suppose we have determined that using a 4-week order interval for replenishing wheat berries is most economical. Now the problem becomes determining how much to order. Since the bakery is open 6 days a week, a 4-week order interval implies a review period of T = 24 (working) days. Orders must be placed on Monday for delivery on Thursday of the same week, so the lead time is L = 3 days. Average demand for wheat is 10 bags per week, so average daily demand is d = 10/6 = 5/3 = 1 2/3 bags per day. From past data, the standard deviation of daily demand is 1/2 bag per day. If the bakery orders too many bags of wheat berries, they will be carried over to the next order interval. Since a bag of flour costs $18 and interest rates are currently very low, the cost to carry a bag of wheat berries for 4 weeks is less than $1. In contrast, running out of wheat berries means that some products will not be able to be baked and business will be lost. The bakery estimates the lost profit on goods baked from a bag of wheat berries to be about $99.

1. What is the optimal service level (probability of not running out) the bakery should strive for on wheat berries?

2. Suppose we approximate demand during T+L by a normal distribution with mean a of 45 bags and standard deviation of 2.6 bags and the bakery currently has 10 bags of wheat berries on a Tuesday when it is time to order. How many bags should they order?