Question

the b&s novelty and craft shop in bennington, vermont, sells a variety of quality, handmade items to tourists. it will sell 600 hand - carved miniature replicas of a colonial soldier each year, but the demand pattern during the year is uncertain. the replicas sell for $60 each, and b&s uses a 10 - percent annual inventory - holding cost rate. ordering costs are $15 per order, and demand during the lead time follows a normal distribution, with a mean of 10 and a standard deviation of ten.
a. what is the recommended order quantity? round your answer to the nearest whole number.
eoq: units
b. if b&s is willing to accept a stockout roughly twice a year, what reorder point would you recommend? what is the probability that b&s will have a stockout in any one order cycle? use appendix a to determine z - value. round z - value to two decimal places. do not round intermediate calculations. round your answer for the reorder point to the nearest whole number and for the probability of a stockout to four decimal places.
reorder point: units
probability of a stockout:
c. what is the safety stock level and annual safety stock costs for this product? do not round intermediate calculations. round your answer for the safety stock level to the nearest whole number and for the safety stock costs to the nearest dollar.
safety stock level: units
safety stock costs: $

Explanation:

Step1: Calculate the probability of a stockout

The number of order cycles per year \(n=\frac{D}{Q}\), where \(D = 600\) (annual demand) and \(Q = 55\) (order quantity from part a). So \(n=\frac{600}{55}\approx10.91\)

If the number of stock - outs per year is \(S = 2\), then the probability of a stockout \(P=\frac{S}{n}\)

Substitute \(S = 2\) and \(n\approx10.91\) into the formula: \(P=\frac{2}{10.91}\approx0.1833\)

Answer:

\(0.1833\)