A food company is attempting to set the customer service level (in-stock probability in its warehouse) for a particular product line item. Annual sales for the items are 100,000 boxes, or 3,846 boxes biweekly. The product cost in inventory is $110 per box, to which $11 is added as profit margin. Stock replenishment is every two weeks and the demand during this time is assumed normally distributed with a standard deviation of 400 boxes. Inventory carrying costs are 30 percent per year of item value.
Management estimates that a 0.156 percent change in total revenue would occur for each 1 percent change in the in-stock probability. Based on the information, find the optimal in-stock probability for the item.