Please answer the question on the computer. If handwriting is required, please do not use connected characters. Thank you for your understanding and time

b$.$ How long does a customer have to wait, on average, before talking to Tom?

c$.$ What is the average total cost of telephone lines over an $8-$hour shift? Note that the

department store is billed whenever a line is in use, including when a line is used to put

customers on hold.

Hint: The easiest way is to first calculate the average number of lines in use, which is equal

to the average number of customers in the system $($both waiting and talking to Tom$),$ i$.$e$.,$

$I=I_q+I_p.$ Then the hourly charge is $($ $$6$ per hour per line$)$ times I lines, and the total

charge over an $8-$hour shift is $8$ times the hourly charge.Question points$)$

The following situation refers to Tom Opim, a first$-$year MBA student. In order to pay the rent,

Tom decides to take a job in the computer department of a local department store. His only

responsibility is to answer telephone calls to the department, most of which are inquiries about

store hours and product availability. As Tom is the only person answering calls, the manager of

the store is concerned about queuing problems. Currently, the computer department receives an

average of one call every $5$ minutes, with a standard deviation in this interarrival time of $3$

minutes. Tom requires an average of $3$ minutes to handle a call. The standard deviation in this

processing time is $1$ minute. The telephone company charges $$6\mathrm{.}00$ per hour for the telephone

lines whenever they are in use $($either while a customer is in conversation with Tom or while

waiting to be helped$).$ Assume that there are no limits on the number of customers that can be on

hold and that customers do not hang up even if forced to wait a long time.

a$.$ For one of his courses, Tom has to read a book $($The Pole, by E$.$ Silvermouse$).$ He can read

$1$ page per minute. Tom's boss has agreed that Tom could use his idle time for studying,

as long as he drops the book as soon as a call comes in$.$ How many pages can Tom read

during an $8-$hour shift?

Hint: You need to calculate the $\%$ of time that Tom is not serving a customer, i$.$e$.,$ idling

$($think about the meaning of utilization$).$ Then, the total idle time in an $8-$hour shift equals

$(8$ hours$)*$ of idle time$).$ From there, you can get how many pages on average Tom can

read during an $8-$hour shift.