1. The variable cost to procure an item (i.e., c) is $ 10. The fixed ordering cost (i.e., K) is estimated to be $ 7.20 per order and the annual per unit carrying charge (i.e., I) is 20 %. Based on this information, consider the following scenarios.

a. Assuming a constant annual demand (i.e., λ) of 12000 units, answer the following questions independently of one another:

i. What is the economic order quantity (Q*)?

ii. What is the Total Annual Costs and Total Annual Relevant cost of ordering Q* units?

iii. If the lead time is 0.25 months, what is the reorder point?

iv. If the annual penalty cost of a backorder (i.e., p) is $ 3.50, what is the optimal order quantity Q* and the optimal backordered quantity B*?

b. Assume 50 working weeks in a year and weekly demand which is normally distributed with a mean of 240 and standard deviation of 50. Then assuming a lead time of 2 weeks, determine the optimal order quantity Q* and corresponding optimal reorder point R* for:

i. A type 1 service level target of 96%; and

ii. A type 2 service level target of 96%.