1. Consider the inventory planning problem where a retailer experiences a demand for a product following Poisson Distribution with Lambda = 5 units.

The retailer incurs a cost of $4 per unit per day if there is excess inventory. However, the retailer will incur $12 per unit per day, if there is a shortage (negative inventory) of up to 3 units, if more than 3 units, then the retailer will incur a fixed $15 if there is a shortage of 4 or more units (i.e., as long as the shortage is 4, 5, 6, etc, the total per day cost is $15, irrespective of how many units were short beyond 3 units).

The retailer's supplier can only supply a maximum of only 7 units per day. But the supplier will only sell if the retailer orders 2 or more units per order, else the supplier will not sell anything that day.

The retailer is interested in determining an optimal ordering policy so that the total cost of inventory holding and shortage is minimal.

1. Find the long-run average cost for the retailer, if she orders 7 units whenever the inventory level drops to zero.
2. Find the long-run average cost for the retailer, if she orders 6 units whenever the inventory level drops to zero.
3. Find the long-run average cost for the retailer, if she orders 5 units whenever the inventory level drops to zero.
4. Find the long-run average cost for the retailer, if she orders 4 units whenever the inventory level drops to zero.
5. Find the long-run average cost for the retailer, if she orders 3 units whenever the inventory level drops to zero.
6. Find the long-run average cost for the retailer, if she orders 2 units whenever the inventory level drops to zero.
7. From the above four questions, identify the best policy for the retailer.