Reference no: EM132813514

MyAccountant.com is a recent start-up trying to cater to customers in search of accounting services who are intimidated by the idea of talking to an accountant or simply too lazy to go to an accountant's office. Unlike traditional accounting firms, MyAccountant.com allows for extensive interaction between accountants 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 accountants (in fact, the firm hires accountants who are graduates of the Leventhal School) customers are encouraged to send emails to [email protected]. From there, the incoming emails are distributed to the accountant who is currently "on call". Given the broad skills of Leventhal graduates, each accountant can respond to each incoming request.
Emails arrive from 8am to 6pm at a rate of 8 emails per hour, with the inter-arrival times are exponentially distributed. At each moment in time, there is exactly one accountant "on call", i.e. sitting at his/her desk, waiting for incoming emails. It takes the accountant, on average, 6 minutes to write the response email, with a standard deviation of 7 minutes.

a) How many emails will an accountant have received at the end of a 10-hour day? (Show your work.)

b) What is the average time (in minutes) a customer has to wait for a response to her email, ignoring any transmission time? (Show your work.)

c) What fraction of time is an accountant idle? (Show your work.)

d) While not responding to emails, the accountant on call is encouraged to actively work on regular business (other client's work; not internet queries) that will bring in revenues to the firm. How much time over a 10-hour day can an accountant dedicate to this activity? (Show your work.)