Supply Chain Management Managment Question $1(10$ points$)$: consider the line flow process consisting of three resources shown in the spreadsheet template.

a$.$ Which resource is the bottleneck of the process? Show your analysis.

b$.$ If demand arrives at $8$ units per hour, what is the process utilization? Assume that input is not constraining the process.

Question $2(15$ 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 $3$ minutes, with a standard deviation in this inter$-$arrival time of $3$ minutes. Tom requires an average of $2$ minutes to handle a call. The standard deviation in this activity time is $1$ minute.

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

b$.$ For one of his courses, Tom has to read a book. 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?

Question $3(25$ points$)$: RentAPhone is a new service company that provides European mobile phones to American visitors to Europe. The company currently has $80$ phones available at Charles de Gaulle Airport in Paris. There are, on average, $25$ customers per day requesting a phone. These requests arrive uniformly throughout the $24$ hours the store is open. The corresponding coefficient of variation is $1.$ Customers keep their phones on average $72$ hours. The standard deviation of this time is $100$ hours.

a$.$ What is the average number of telephones the company has in its store?

b$.$ How many customers, on average, are waiting for the phone?

c$.$ What is the average waiting time per customer if the company decides to limit all rentals to exactly $72$ hours? Assume that if such a restriction is imposed, the number of customers requesting a phone would be reduced to $20$ customers per day $($everything else is kept the same as before$).$apacit