Daily demand for fresh cauliflower in the ZZ-Warehouse store follows normal distribution with mean 100 cartons and s.d.20 cartons.The ZZ-Warehouse buys at a cost of $50.00 per carton, 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 square root of the product of the demand variance and the order cost divided by the unit profit. In this case, the demand variance is 20^2 = 400, the order cost is $50.00, and the unit profit is $70.00 - $50.00 = $20.00. Therefore, the safety stock is sqrt(400 * $50.00 / $20.00) = 20 cartons. The optimal order quantity is therefore 100 + 20 = 95 cartons.

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