Response to the following problem:
Daily Fax Incorporated (DFI) is an automated information system that operates as follows: Customers call an 800 phone number and input their fax number and information request (sports scores, stock market information, topical cartoons, jokes) using a touch-tone telephone. The computer then faxes a one-page sheet of paper containing the requested information as well as approximately a quarter page of advertising. The company earns its profits from the advertising revenue as well as from a directory of fax numbers that it publishes monthly (based on the fax numbers it receives from callers). The Daily Fax computer system is set up so that there are sufficient telephone lines to answer all incoming phone calls. However, there is only one outgoing fax transmission line. The total time to process each incoming fax request is exactly 25 seconds. Calls come into Daily Fax according to a Poisson process at an average rate of 2 per minute. DFI would like to be able to inform potential advertisers of the average time a customer must wait for a fax to arrive.
a. What assumptions would you make to model this problem?
b. Given these assumptions, what is your estimate of average time (in minutes) a customer must wait for a fax?