Daily demand for fresh cauliflower in the ZZ-Warehouse store follows a normal distribution with a mean of 100 cartons and standard deviation of 20 cartons. The ZZ-Warehouse buys at a cost of $50.00 per carton and sells it for $70.00 per carton. Unsold cartons are sold for $20.00 per carton. What is the optimal order quantity, using the single-period model?
A) 100
B) 80
C) 95
D) 110
E) 105

Question

Quizplus · Accepted Answer

The optimal order quantity is 95 cartons. This is because the expected profit is maximized when the order quantity is equal to the mean demand plus the safety stock. The safety stock is calculated as the product of the standard deviation of demand and the z-score corresponding to the desired service level. In this case, the desired service level is 95%, which corresponds to a z-score of 1.645. Therefore, the safety stock is 20 * 1.645 = 32.9 cartons. The optimal order quantity is therefore 100 + 32.9 = 95 cartons.

Daily Demand for Fresh Cauliflower in the ZZ-Warehouse Store Follows