First City Bank orders cash from the Federal Reserve Board to meet daily transaction needs. Linda Davis, the operations manager, estimates that $5,000,000 in cash will be needed next month. She has estimated that the cost to order, receive, and store each shipment of cash from the Federal Reserve Board will be $675 per shipment. First City Bank is open for business 250 days each year. These are considered its working days for the year. The bank’s related carrying cost for cash is 0.65 percent per month. That is, each dollar held in the bank’s vault costs $0.0065 per month in foregone profits.

a) How much should Linda order from the Federal Reserve Board each time a cash order is placed if she wants to minimize her cost?

b) What is the expected total annual holding cost plus ordering cost?

c) If the lead time is 3 days what is the reorder point? Also, what is the inventory position immediately after reordering?  

d) If it is against First City Bank’s policy to order more than $750,000 when placing a cash order. How much should it order each time? Explain or support your answer.