In a local department store bi-weekly sales for an item is 500 units. The product cost in inventory is $20, to which $2 is added as profit margin. The stock is replenished every two weeks and standard deviation of demand during this time is 100 units. Inventory carrying cost is 25 percent per year of items cost. Management estimates that 0.25% change in sales would occur for each 1 percent change in the service level (i.e., in stock probability).

a) Based on above information, find the optimum service level (i.e., in stock probability) for the item.

b) What is the limitation (i.e., weakest assumption) of this analysis methodology?