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Cms 201: Operations Research I Question Paper

Cms 201: Operations Research I

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2009

1
UNIVERSITY EXAMINATIONS: 2008/2009
SECOND YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 201: OPERATIONS RESEARCH I
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Briefly describe the nature of operations research (4 Marks)
b) State four assumptions of linear programming (4 Marks)
c) Duplex textile ltd makes executive and standard dresses. An executive dress requires 60
minutes for cutting, 50 minutes for sewing, 40 minutes for finishing and 15 minutes for
inspection and packaging. A standard dress requires 42 minutes for cutting, 30 minutes for
sewing, 60 minutes for finishing and 6 minutes for inspection and packaging.
The firm employs 35 tailors who spend a maximum of 630 hours for cutting, 600 hours for
sewing, 708 hours for finishing and 135 hours of inspection and packaging every week. The
profit contribution per dress is sh 1,500 for the executive dress and sh 1,350 for the standard
dress.
Required
Formulate the linear programming model (6 Marks)
d) Discuss the limitations of the Economic order quantity model (4 Marks)
2
e) Rapid Fit Ltd. is a modern quick motor service centre in Kampala. It has a single engineer and
a technician. The Engineer can attend to incoming cars at a rate of 8 per hour. Cars enter the
centre randomly at a rate of 6 per hour.
Required:
i) What is the average number of cars at the centre? (2 Marks)
ii) What is the average number of cars waiting for the Engineer? (2 Marks)
iii) What average time per car is spent in the queuing system? (2 Marks)
iv) What is the probability that the Engineer will be idle? (2 Marks)
f) Explain the following terms as used in network analysis:
(i) Network planning ( 2 Marks)
(ii) Critical path ( 2 Marks)
QUESTION TWO
a) A baker makes two products, large loaves and small round loaves. He can sell up to 280 of the
large loaves and up to 400 small round loaves per day. Each large loaf occupies o.o1m3 of
shelf space, each small loaf occupies 0.008m3 of space and there is 4m3 of shelf space
available. There are 8 hours available each night for baking, and he can produce large loaves
at the rate of 40 per hour, and small loaves at the rate of 80 per hour. The profit on each large
loaf is Sh.5 and Sh.3 profit on the small round loaf.
Required:
In order to maximize profits, how many large and small round loaves should he produce?
(17 Marks)
b) Summarize the procedure for solving the kind of quantitative technique you have used to solve
part (a) above. ( 3 Marks)
(Total: 20 Marks)
QUESTION THREE
a) Explain the difference between assignment and transportation problems. (4 Marks)
b) State the assumptions made in solving a transportation problem. (4 Marks)
c) Umoja Engineering Works Ltd. has a network of branches all over Kenya. The branches are
used to service, repair and install equipment for their clients. Currently, the Nairobi branch
3
has four clients who require installation of equipment. Each client requires the services of one
engineer.
There are four engineers who are not engaged at the moment and can be assigned any one of
the tasks. However, these engineers have to travel from different locations and the Nairobi
branch has to meet their travel and subsistence allowances. The allowances vary from one
engineer to another and according to the client the engineer has been assigned to work for.
The table below shows the costs (in thousands of shillings) associated with each engineer.
Client
Engineer 1 2 3 4
A
B
C
D
37
57
22
39
27
22
25
42
34
79
61
54
21
34
45
43
Required:
a) The assignments to be made in order to minimize the total cost of the engineers.
(10 Marks)
b) The minimum cost of using the engineers. (2 Marks)
(Total: 20 Marks)
QUESTION FOUR
Kiko Ltd. is a large cash and carry warehouse which sells electronics. Kiko Ltd. purchases the most
popular model of calculators (FX 100) directly from the manufacturer at a cost of Sh.250 each.
Average sales per a 300 day year are 475 calculators. Whenever an order with the manufacturer is
placed, Kiko Ltd. incurs a cost of Sh.50. The stock holding costs are estimated at Sh.12.50 plus 10%
opportunity cost of capital. The lead time is three days. During the last 50 stock cycles, the demand
during the lead time has generated the following frequency distribution:
Lead time demand 0 1 2 3 4 5 6 7 8
Number of stock cycles 1 2 6 8 10 8 8 5 2
Each time the warehouse runs out of stock, an emergency order is placed with an extra cost of Sh.20
per calculator.
4
Required:
(a) The economic order quantity (EOQ) (4 Marks)
(b) The number of orders per annum (2 Marks)
(c) The optimal safety stock level (12 Marks)
(d) The revised reorder level. (2 Marks)
(Total: 20 Marks)
QUESTION FIVE
A construction project consists of the activities shown below:
Activities
Time (weeks)
Optimistic Most likely Pessimistic
1 – 2
1 – 3
2 – 4
2 – 5
3 - 4
4 – 5
4 – 6
5 – 6
6 – 7
4
3
7
3
6
4
3
2
3
6
5
12
5
11
6
9
4
5
10
9
20
8
15
11
14
8
9
Required:
a) The expected time and variance of each activity. (6 Marks)
b) A project network for the activities. (6 Marks)
c) The expected completion time and variance of the project. (2 Marks)
d) If the project is completed in less than 30 weeks, it will cost Sh.1.0 million. It will cost
Sh.1.5 million if the project is completed between 30 and 35 weeks and Sh.2.0 million if it
takes more than 35 weeks. Compute the expected cost of the project. (6 Marks)
(Total: 20 Marks)

Cms 201: Operations Research I Question Paper

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