The annual demand for one inventory item is constant and known with certainty to be 12,000 units. Currently the item is procured from a supplier with a variable ordering cost per unit of $ 10. The fixed ordering cost is estimated to be $ 7.20 per order and the annual per unit holding cost is 20 % of the variable ordering cost per unit. Answer each of the following problems independently of one another:

a. Compute the optimal order quantity and the corresponding Total Annual Relevant Costs, and Total Annual Costs.

b. If the item could be backordered with an annual penalty cost/unit of $ 3.50, determine the optimal order quantity and the optimal amount backordered.

c. If the same item could be procured for a price of $ 9.90 per unit from another source provided the order size is 950 or more (i.e., an all units discount scheme), would you accept this offer? Provide all relevant calculations to support your answer.

d. Assume another external supplier offers the following incremental pricing scheme: (a) if the order size is 900 units or less, then the price will be $ 10 per unit; and (b) if the order size exceeds 900 units every additional unit will be priced at $ 9.95 per unit. Would you accept this offer? Provide all relevant calculations to support your answer.