A study aid desk manned by a graduate student has been established to answer student’s questions and help in working problems in your OM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour, and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS.
Using this information, answer the following questions.

a. Calculate the percent of utilization of the graduate student P= 4/6 = 2/3 = . 6667 percent utilization
b. Determine the average number of students in the system ?= 4 per hour ?= 6 students helped an hour Ls= 4/ 6-4 = 4/2 = 2 students in the system on average.
c. Calculate the average time in the system Ws= 1/ 6-4 =? =. 5 hours average time in the system
d. Find out the probability of four or more students being in line or being served P0= 1 – 4/6 = 1- 2/3 =. 33 probability that there are 4 or more students being in line or being served.

Before a test, the arrival of students increases to five per hour on the average. Compute the average number of students waiting under this scenario.
Lq= 4^2 / 6 (6-4) = 16/ 12= 1. 33
Students waiting in line on average. What are the three characteristics of awaiting? Line system?

Arrivals or inputs to the system: these have characteristics such as population size, behavior, and statistical distribution.
Queue discipline, or the waiting line itself: characteristics of the queue include whether is it limited or unlimited in length and the discipline of people or items in it.  The service facility: its characteristics include its design and the statistical distribution of service times.

Question 2.
Radovilsky’s Department Store in Haywood, California, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited for the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order at an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The cost of the clerk is $10 per hour, but because of lost goodwill and sales, Radovilsky loses about $25 per hour of customer time spent waiting for the clerk to take an order. ?= 12 ? = 15.

(a) What is the average time that catalog customers must wait before their calls are transferred to the order clerk? Wq= 12/ 15 (15-12) = . 2667 average time to wait before transferring.
(b) What is the average number of callers waiting to place an order? Lq = 12^2 / 15 (15- 12) = 3. 2 average number of callers waiting to place an order.
(c) Radovilsky’s is considering adding a second clerk to take calls. The store’s cost would be the same at $10 per hour. Should it hire another clerk? Explain your decision. Yes, they should hire another clerk because the customer average wait time and the average number of callers waiting to place an order indicate that a second representative is needed.

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