A bank offers a credit card that can be used in various locations

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  months after credit is issued increases at a decreasing rate. Historical data suggest the following function:

The average credit issued in any 1 month is $125 million, and historical experience suggests that for new credit issued in any month, collection efforts cost $1 million/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?

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