Get premium membership and access revision papers, questions with answers as well as video lessons.
Got a question or eager to learn? Discover limitless learning on WhatsApp now -
Start Now!
Cpa Section Iv - Quantitative Analysis. Question Paper
Cpa Section Iv - Quantitative Analysis.
Course:
Institution: Royal Business School question papers
Exam Year:2011
QUEUEING THEORY PROBLEMS.
QUESTION ONE
The wheat harvesting season in the American Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the recieving bin. The central bin is owned cooperatively, and it is ve every farmer''s benefit to make the unloading/storage process as efficiently as possible. The cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The storage bin is open and operated 16 hours per day and 7 days per week during the harvest season and is capable of unloading 35 trucks per hour according to an exponential distribution. Full trucks arrive all day long at a rate of about 30 per hour, following a Poisson pattern.
To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, find the:
a. Average number of trucks in the unloading system.
b. Average time per truck in the system.
c. Utilization rate for the bin area.
d. Probability that there are more than three trucks in the system at any given time.
e. Total daily cost to the farmers of having their trucks tied up in the unloading process.
f. The Cooperatives, as mentioned, uses the storage bin only 2 weeks/year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off-season. Would it be worth the Cooperative''s while to enlarge the storage area?
QUESTION TWO
A company store room can serve 12 maintenance employees per hour on the average. They arrive at the storeroom at an average rate of one every 6 mins. The maintenance employees earn $6 an hour and the clerk who runs the storeroom, $10 an hour.
Find:
a. The average number of maintenance employees waiting for service and being served.
b. The average number of maintenance employees in the waiting line.
c. The average time a maintenance employee will be in the waiting line (before being served, in mins)
d. It takes a maintenance employee 3 minutes to walk from his work area to the storeroom. Find the average time a maintenance employee will be away from his working area each time he goes to the storeroom. (Answer in mins)
e. The chance (in percent) of there being no ''customers'' at the storeroom.
f. The chance (in percent) that more than 3 ''customers'' will be in the storeroom area (both waiting and being served)
g. The probability (in percent) that fewer than 4 employees will be in the storeroom area (both waiting and being served)
h. The boss has complained about the "crowd" of "goldbrickers" around the storeroom, and told the foreman to get them back to work-at no extra cost to the company-or else!
The foreman has three choices:
One is to add a second clerk to help serve in the storeroom, working as a team with the original clerk, and receiving $10 an hour, as well. Then an average of 15 employees could be served each hour.
Or else he can split the storeroom into two and let the two clerks operate independent, equal facilities, each with the original 12-per-hour service rate (together serving one line on a first-come, first-served basis). This independent set up would cost an additional $12 an hour.
Or else he can quit. Can he keep his job? How?
QUESTION THREE
The engine department of Bilge Corp. repairs large motors for the entire corporation. Motors arrive at the shop every 6 hours. When a motor is not running, the Bilge Corp. loses $20 per hour. The engine department works on two 8-hour shifts, 6 days a week, 50 weeks a year. The company is considering 2 alternatives for the engine department:
a. Build a large repair line, which will cost $250,000/year (operation, maintenance, depreciation). Such a line can repair 4 motors in one shift.
b. Build two small parallel lines, at a total cost of $220,000. The repair time, per motor, will be 4 hours, in either line. The parallel system will serve one waiting line.
Find the alternative which will minimize the total cost for Bilge.
QUESTION FOUR
Customers arrive at an automated coffee vending machine at a rate of 4/min, following a Poisson distribution. The coffee machine dispenses a cup of coffee in exactly 10 seconds.
a. What is the average number of people waiting in line?
b. What is the average number in the system?
c. How long does the average person wait in line before receiving service?
QUESTION FIVE
Trains arrive at the yard every 15 minutes and the service time is 33 minutes. If the line capacity of the yard is limited to 4 trains, find
i. The probability that the yard is empty.
ii. The average number of trains in the system.
More Question Papers
Popular Exams
Return to Question Papers