Your bank account consists of a checking and savings accounts. Assume your expenses and earnings can be described by a random walk with an equal probability to spend one dollar or to receive one dollar in your checking account at every time interval. You are charged $5 for any transaction from the checking account to the savings account and viceversa. Also, assume that the cost per unit of cash, per unit of time r of keeping cash on hand is equal to $0.1 dollars for any dollar on hand per time period.

Determine: (A) The optimal values of the two thresholds s and S, i.e., the amount of cash in your checking account restored after each transaction, and the maximum amount of cash in your checking account, respectively.

(B) The long run average cost associated to the optimal cash management strategy and to the strategy with the same s but with a maximum amount of cash equal to 2 S.

(C) Please provide some criticism to this model based on your experience