Consider that a manufacturer has an inventory of two replacement parts for two pieces of equipment that often fails. Part 1 costs $175 and has demand of 8 per month. Part 2 costs $20 and has demand of 25 per month (a month is 30 days). The lead time for Part 1 is 30 days and for Part 2 is 15 days. Answer the following questions below using this information.

1. Assume demand is Poisson distributed, what base stock is required for Part 1 and Part 2 so that a fill rate of 98% is achieved (show your table and submit your excel file for the Poisson distribution). Calculate the expected backorders and on-hand inventory for each part given this Q* values and a service level of 98%
2. Assume holding cost is 3% per month and order costs are $5. What is the Q* using EOQ for each part? Is there a difference in the expected backorder level and on-hand inventory? If different, explain.
3. Assume backorder cost per unit per month is $10, recalculate reorder points. Now, using Q values from part b compare average on-hand inventory and backorder level.

d. Explain how you would modify the model(s) if lead time is variable