My-law.com is a recent start-up trying to cater to customers in search of legal services who are intimidated by the idea of talking to a lawyer or simply too lazy to enter a law office. Unlike traditional law firms, My-law.com allows for extensive interaction between lawyers and their customers via telephone and the Internet. This process is used in the upfront part of the customer interaction, largely consisting of answering some basic customer questions prior to entering a formal relationship. In order to allow customers to interact with the firm's lawyers, customers are encouraged to send e-mails to my-lawyer@My-law.com. From there, the incoming e-mails are distributed to the lawyer who is currently "on call." Given the broad skills of the lawyers, each lawyer can respond to each incoming request. E-mails arrive from 8 AM. to 6PM . at a rate of 10 e-mails per hour (coefficient of variation for the arrivals is 1). At each moment in time, there is exactly one lawyer "on call," that is, sitting at his or her desk waiting for incoming e-mails. It takes the lawyer, on aver- age, 5 minutes to write the response e-mail. The standard deviation of this is 4 minutes.
a. What is the average time a customer has to wait for the response to his/her e-mail, ignoring any transmission times?
b. How many e-mails will a lawyer have received at the end of a 10-hour day?
c. When not responding to e-mails, the lawyer on call is encouraged to actively pursue cases that potentially could lead to large settlements. How much time on a 10-hour day can a My-law.com lawyer dedicate to this activity (assume the lawyer can instantly switch between e-mails and work on a settlement)? To increase the responsiveness of the firm, the board of My-law.com proposes a new operating policy. Under the new policy, the response would be highly standardized, reducing the standard deviation for writing the response e-mail to 0.5 minute. The average writing time would remain unchanged.
d. How would the amount of time a lawyer can dedicate to the search for large settlement cases change with this new operating policy?
e. How would the average time a customer has to wait for the response to his/her e-mail change?