Talisman Games, a local gaming store, stocks the 4th edition of the rulebook of a popular pen-and-paper role-playing game -Daggers and Dungeons. Talisman orders the rulebooks directly from its publisher -Wizards of the Shore (WotS). The fixed order cost is $20 per order. Demand for the rulebook each week is 4 units with no variability. Talisman estimates that the average cost of managing the inventories is about $5 per unit per week.

Q1. What is Talisman's optimal inventory control policy; that is, its optimal order quantity Q*?

Q2. What is the average inventory of the rulebooks in Talisman? How long on average does a rulebook spend in Talisman before it is sold to a customer?

This morning a sales rep from WotS contacted the owners of Talisman. The owners learn that the new 5th edition of Daggers and Dungeons will be released in exactly 12 weeks. The sales rep told them that today was their last chance to order 4th edition books before they go out of print.

Talisman forecasts that starting from today, the weekly demand for the 4th edition will follow a normal distribution with a mean of 4 units and a standard deviation of 2 units until the 5th edition is released. Assume that the demands for each week are i.i.d. Besides the cost of managing the inventories, Talisman finds that ordering the rulebook from WotS has a cost of $9. Talisman can sell to the customers at a price of $20. After 5th edition is released, they will have to sell the 4th edition book by only 20% of the original market price to sell the remaining units (assume all are eventually sold at this reduced price).

Q3. What inventory level for 4th edition books should Talisman target to have in the last order?