E. J. Korvair Department Store is trying to determine an optimal cash management policy.

During each day, the demand for cash may be described by a random variable D, where p(D 

d)  p(d). At the beginning of each day, the store sends an employee to the bank to deposit or withdraw funds. Each bank transaction costs K dollars. Then E. J.’s demand for cash is met by cash left from the previous day plus money withdrawn (or minus money deposited). At the end of the day, the store determines its cash balance at the store. If the cash balance is negative, a shortage cost of s dollars per dollar short is incurred.

If the ending balance is positive, a cost of i dollars per dollar held is incurred (be- cause of loss of interest that could have been earned by depositing cash in the bank). At the beginning of day 1, the store has $10,000 cash on hand and a bank balance of

$100,000. Formulate a dynamic programming model that can be used to minimize the expected cost of filling the store’s cash needs for the next 30 days.