Tom and Stacy work together to order items for a large clothing retailer. They disagree about ordering a popular jeans brand from Italy. The demand for the jeans is variable and follows Normal distribution. They use (Q, R) policy to manage their inventory. Stacy suggests that they should order 200 pairs when their inventory reaches or falls below 50. While Tom agrees that the order size should be 200, he thinks that they should place an order when their inventory reaches or falls below 80.

4. Tom in Problem 3 argues with Stacy that, if they place an order when the inventory reaches or falls below 50 (as Stacy suggests), then they need to increase their order size to 230. Explain why each of the following statements is true or false.

a. Under Toms new policy (i.e., ordering 230 when inventory reaches 50) the likelihood of shortage is less than that under Stacys policy.

b. The fraction of customers who face shortage under Toms new policy is the same as that under Stacys policy.

c. Stacys policy is expected to result in more number of orders placed in a year.

d. Toms new policy results in lower average shortage cost in a year.

e. Toms policy results in lower expected annual inventory holding cost in a year.