A manufacturing company keeps stock of replacement parts for its critical equipment. The lead time for a rare $500 part is 2 months. The maintenance manager keeps close track of the inventory of these parts and places a new order whenever the stock reaches a certain threshold or reorder point. When they order, they place orders of 20 units at a time because the supplier has to make a special production run for it. From past history they estimate that the monthly demand for spares can be modeled as a Poisson distribution with a mean of 3.

a) Calculate the reorder point to achieve a fill rate of 95%.

b) Calculate the resulting average backorder level associated with this ordering policy.

c) Calculate the average monthly inventory cost assuming annual carrying cost of 24%.