A small shop wants to analyse its inventory policy for some candles it buys from a supplier in a nearby town. The owner of the store has determined that the annual demand for this product is normally distributed with a mean of 800 candles and a standard deviation of 40. The cost of holding inventory is estimated to be $3 per candle per year. Each time an order is placed, the supplier charges $500 for transport fuel and takes 10 days to deliver the order. In the event that candles are not available and a customer arrives to buy, the customer is put on a waiting list and when they arrive they are shipped to their home, which represents a cost to the shop of $15 per candle per year. assuming the shop works 300 days a year, answer the following:

1. What is the optimal level of service that should be managed?

2. Draw a graph of the behaviour of the inventory level for at least two cycles where you clearly indicate the time between overhauls (or cycle time), the ideal maximum inventory level, the safety inventory and the lead time when you want to minimise cost.

3. Assuming that in one cycle the owner had 5 missing candles (waiting customers), how many candles should he order?

4. Assuming that the owner wishes to have on average only 10 occasions per year Assuming that the owner wishes to have an average of only 10 occasions per year when a customer arrives and there are no candles, what is the level of service the owner is looking for?