An administrator for a major hospital is trying to decide how many units of disposable bedside supplies should be ordered and held next year. The forecasting experts have said that the quarterly number of patient days for next year is 50,000 in the first quarter, 20,000 in the second quarter, 90,000 in the third quarter, and 40,000 in the last quarter. The total number of patient days for next year is forecasted to be 200,000.

Every day that a patient is hospitalized, they receive a set of pre-packaged supplies first thing in the morning or upon check-in. Regardless of use or not, the supply set is disposed and replaced the next day. Each set costs $50. The sole supplier for the product will refill an order immediately but there is a $40 fee for placing an order. One problem for the hospital is storage space. It is found that storing an item costs the hospital $5 over a year.

The administrator comes to you, his favorite fixit person. You seem to have a knack for making the right decisions. What should the hospital do? The head of nursing suggests using the Economic Order Quantity model to determine the optimal number of items to order at a time. Initially you agree, but upon contemplation you think that that model should be amended to account for the quarterly differences.

Using EOQ as in the text, find the Q* and total cost of the policy.