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Cpa Section Iv - Quantitative Analysis. Question Paper
Cpa Section Iv - Quantitative Analysis.
Course:Cpa Part Ii
Institution: Royal Business School question papers
Exam Year:2011
CPA SECTION IV - QUANTITATIVE ANALYSIS.
QUEUEING THEORY PROBLEMS.
QUESTION ONE.
A garage has employed a mechanic, Koskei who is able to service a car at an average of 1 car every 20 minutes. Customers needing this service arrive at the garage on average of 2 per hour.
Assuming queueing formulae for the simple queue apply
Required:
Determine the following:
i. The number of cars in the garage waiting to be serviced.
ii. Total number of cars in the garage.
iii. How long a car takes being actually serviced.
iv. The probability that the garage is busy.
v. The probability that there are more than 5 cars in the garage.
vi. The probability that there are 3 or less cars in the garage.
vii. The probability that service time is 25 minutes or less.
viii. The probability that a customer will be in the system for more than 15 minutes.
b. The cost of customer waiting time, in terms of customer dissatisfaction and lost goodwill is Sh. 600 per hour of time spent waiting in line (once customers cars are actually being serviced, they do not seen to mind waiting). Koskei is paid Sh. 420 per hour (the garage is open 8 hours a day).
Due to customer complaint, management of the garage is reviewing Koskei''s performance. An applicant mechanic, Omondi can service 1 car every 15 minutes but he is asking to be paid Sh. 720 per hour.
Required:
By evaluating the relevant costs for Koskei and Omondi, advise management on what to do.
c. Suppose the garage has an option of opening a second bay where another mechanic, Mwanyumba, who can work at the same rate as Koskei can be employed. Assume opening of a second bay does not affect arrival rate. Also assume second bay is costless to open.
Required:
Determine whether this option is desirable.
QUESTION TWO
Mike Dreskin manages a large Los Angeles movie theatre complex called Cinema I, II, III and IV. Each of the four auditoriums plays a different film; the schedule is set so that starting times are staggered to avoid the large crowds that would occur if all four movies started at the same time. The theatre has a single ticket booth and a cashier who can maintain an average service rate of 280 movie patrons per hour. Service times are assumed to follow an exponential distribution. Arrivals on a normally active day are Poisson distributed and average 210 per hour.
In order to determine the efficiency of the current ticket operation, Mike wishes to examine several queue operating characteristics.
Required:
a. Find the average number of moviegoers waiting in line to purchase a ticket.
b. What percentage of the time is the cashier busy?
c. What is the average time a customer spends in the system?
d. What is the average time spent waiting in the line to get to the ticket window?
e. What is the probability that there are more than two people in the system?
QUESTION THREE
Ashley''s Department store in Kansas City maintains a successful catalogue sales department in which a clerk takes order by telephone. If the clerk is occupied on one line, incoming phone calls to the catalogue department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party that has waited the longest is transferred and answered first. Calls came in at a rate of about 12 per hour. The clerk is capable of taking an order in an average of four minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential.
The clerk is paid $5 per hour, but because of lost goodwill and sales, Ashley''s loses about $25 per hour of customer time spent waiting for the clerk to take an order.
a. What is the average time that catalogue customers must wait before their calls are transferred to the order clerk?
b. What is the average number of callers waiting to place an order?
c. Ashley is considering adding a second clerk to take calls. The store would pay the person the same $5 per hour. Should it hire another clerk? Explain.
QUESTION FOUR
One mechanic services 5 drilling machines for a steel slave manufacturer. Machines break down on average of once every 6 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of one repair job per day. Repairs follow an exponential distribution.
a. How many machines are waiting for service, on average?
b. How many are in the system, on average?
c. How many drills are in running order, on average?
d. What is the average waiting time in the queue?
e. What is the average waiting time in the system?
QUESTION FIVE
A technician monitors a group of five computers that run an automated manufacturing facility. It takes an average of 15 minutes (exponentially distributed) to adjust a computer that develops a problem. The computers run for an average of 85 minutes (Poisson distributed) without requiring adjustments. What is the:
a. Average number of computers for adjustment?
b. Average number of computers not working?
c. Probability that the system is empty?
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