1: What is the average total time (lead time) it takes a property law customer to get a response to his/her e-mail?

2: Continuing from the previous question, just consider property law flow. To increase the responsiveness of the firm, the board of My-law.com proposes a new operating policy of highly standardizing the response. This standardization will reduce the standard deviation of the writing time of response e-mail to 0.5 minutes. The mean of service time remains the same 5 minutes. There is no change in the arrival process. Due to this idea, what is the new average total time it takes a customer to get a response?

3: Continuing from the original My-law.com setup (that is, still with Cs=1), and considering just the property law flow, the firm is thinking about hiring another property lawyer, increasing the number of lawyers to handle property emails from 1 to 2. The new lawyer will bring his customer contacts with him and therefore the property email arrival rate will increase from 10/hr to 21/hr. The firm has a goal to keep average wait time for property emails less than 30 minutes. Will hiring another property lawyer help achieve this wait time goal?

[\#3.1, 3.2, 3.3] My-law.com is a recent start-up serving customers in search of legal services in two areas - property law and family law. New customers are encouraged to send emails to the inbox mylawyer@My-law.com and put either property law or family law in the subject line. There are always two lawyers "on call," one property lawyer and the other family lawyer, available to answer emails. Whenever the property lawyer completes a conversation and becomes free, s/ he picks up the oldest email with the subject property law in the inbox. Family lawyer does the same thing with family law emails. E-mails with property in subject line arrive at an average rate of 10 e-mails per hours. E-mails with family in subject line also arrive at an average rate of 10 e-mails per hours. It takes one lawyer (property or family), on average, 5 minutes to write the response e-mail. Assume Ca=1 and Cs=1. [3.1] What is the average total time (lead time) it takes a property law customer to get a response to his/her e-mail? (Note: The lead time includes the time an email waits as well as the actual writing time. Treat two flows (property and family) separately. Answer will be the same for each flow.)