A resort hotel is planning to install a computerized inventory system to manage complementary guest items such as soap and shampoo. The daily demand for bars of soap appears to be distributed normally, with mean = 16 and standard deviation = 3. Assume there are 365 days considered for this inventory system. Once an order is placed, it takes seven days before delivery is made. The effort for the staff person to place an order is $10. The annual holding cost of a bar of soap is $0.05. The hotel is concerned about stock-outs of such a basic item and, thus, desires a 99.9% service level. a. Recommend an order quantity and reorder point for this inventory system.
b. What is the total annual cost for this inventory system?

a) safety stock = z-score x √lead time x standard deviation of demand

z-score for 99.9% = 3.29053

√lead time = √7 = 2.6458

standard deviation of demand = 3

safety stock = 3.29053 x 2.6458 x 3 = 26.12 ≈ 26 soaps

reorder point = lead time demand + safety stock = (7 x 16) + 26 = 138 soaps

EOQ = √[(2 x S x D) / H]

S = order cost = $10

D = annual demand = 16 x 365 = 5,840

H = $0.05

EOQ = √[(2 x $10 x 5,840) / $0.05] = 1,528.40 ≈ 1,528 soaps

b) total order costs per year = (5,840 / 1,528) x $10 = $38.22

total holding costs = (1,528 / 2) x $0.05 = $38.20

total annual ordering and holding costs = $76.42

answer; the nav calculated at the market close at 4: 00 pm new york time;

answer; by looking at total product,marginal product,and changes in both after changes in inputs