Hello tutor, can you please help solve the questions Im stucked with. Would appreciate if you can leave an explanation too. Thank you Question 1, Need help with “b” The organizers of a conference in the Houston Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers and only one person uses a computer at a time. On average there are 30 attendee arrivals per hour and the average time a person spends on the computer is 10 minutes a) To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn’t exceed 80 percent. At least how many computers do they need to have? Answer: Utilization = 30/ (0.8*6) = 6.25 computers Rounded up to 7 Computers b) The organizers of the conference have decided to buy 10 computers. Assume that the standard deviation of arrivals is equal to the average inter-arrival time, and the standard deviation of processing times is equal to the average processing time. What is the average waiting time (in minutes) to check e-mails? Question 2, Need help with “B & C” 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 4 minutes, with a standard deviation in this interarrival time of 2 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 $6.00 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. a. How many pages can Tom read during an 8-hour shift? Hint: 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. –> Service time (S) = 3 minutes Utlization = ¼ / ⅓ = ¾ Idle time = (1-3/4 ) x 480 = (¼) x 480 = 120 minutes Answer: 120 pages 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. Question 3, not sure if answer is correct for A & B, need help from C-E Atlantic Video, a small video rental store in Philadelphia, is open 24 hours a day, and-due to its proximity to a major business school-experiences customers arriving around the clock. A recent analysis done by the store manager indicates that there are 40 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. This arrival pattern is consistent and is independent of the time of day. The checkout is currently operated by one employee, who needs on average 1 minute to check out a customer. The standard deviation of this check-out time is 3 minutes, primarily as a result of customers taking home different numbers of videos. a. If you assume that every customer rents at least one video (i.e., has to go to the checkout), what is the average time a customer has to wait in line before getting served by the checkout employee (i.e., waiting time in queue)? –> p = 1 a = 2 minutes u = p/a = 0.5 Cva = 1 Cvp = 3/1 = 3 Waiting time = 1 min * [0.5/(1-0.5)] * [(1^2+3^2)/2] = 6 min b. If there are no customers requiring checkout, the employee is sorting returned videos, of which there are always plenty waiting to be sorted. How many videos can the employee sort over an 8-hour shift (assume no breaks) if it takes exactly 1.5 minutes to sort a single video? –> Idle time = 2 – 1 = 1 minutes per customer Total idle time = 1 x 8 hours x 60 minutes / 2 per customer = 240 minutes 240/1.5 = 160 videos c. What is the average number of customers who are at the checkout desk, either waiting or currently being served? d. Now assume for this question only that 10 percent of the customers do not rent a video at all and therefore do not have to go through checkout. What is the average time a customer has to wait in line before getting served by the checkout employee (i.e., waiting time in queue)? Assume that the coefficient of variation for the arrival process remains the same as before. e. As a special service, the store offers free popcorn and sodas for customers waiting in line at the checkout desk. (Note: The person who is currently being served is too busy with paying to eat or drink.) The store owner estimates that every minute of customer waiting time costs the store 75 cents because of the consumed food. What is the optimal number of employees at checkout? Assume an hourly wage rate of $10 per hour, and all customers need to check out (i.e., disregard part (d)).