Collecting Credit Card Debt A bank offers a credit card that can be used in various locations. The bank's analysts believe that the percentage P of accounts receivable collected by t months after credit is issued increases at a decreasing rate. Historical data suggest the following function:
P = 0.9[1 - exp(-0.6t)]
The average credit issued in any one month is $125 million, and historical experience suggests that for new credit issued in any month, collection efforts cost $1 million per month.
(a) Determine the number of months that collection efforts should be continued if the objective is to maximize the net collections (dollars collected minus collection costs). Allow for fractional months.
(b) Under the optimal policy in (a), what percentage of accounts receivable should be collected?