Question 3. (20 points) Demand of Double Espresso Scuro for Nespresso machine follows a Normal distribution with the mean of 5000 packs per month (each pack includes 10 capsules) and the standard deviation of 500 packs. The lead time is 15 days from time of ordering to delivery. Assume continuous review inventory system with the order size of 8000 packs and it is desired to satisfy the demands in at least 95% of the lead time periods. Obtain the followings in packs and assume each month includes 30 days.

a) The safety stock of Double Espresso Scuro

b) The reorder point of Double Espresso Scuro

c) The average inventory of Double Espresso Scuro

Question 4. (30 points) Assume the inventory system of question 3, with the same demand and lead-time. Assume that the ordering cost is $100 and the unit inventory holding cost is $2 per pack per year. If the desired fill rate is 98% then,

a) Obtain the optimal order size and reorder point.

b) What is the imputed shortage cost?

c) What will be the optimal order size and reorder point if the lead time be a random variable with the mean of 15 days and standard