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Cms 201: Operation Research I Question Paper
Cms 201: Operation Research I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2009/2010
SECOND YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 201: OPERATION RESEARCH I (DAY + EVENING)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions.
Normal distribution table is attached at the end of the question paper
QUESTION ONE
a) The Daltex oil company has three oil refineries. These refineries are currently operating at less
than maximum capacity. The company has the opportunity to sell certain oil products to a
competing oil company. Since the competing firm has an alternative source of supply, the sale will
not change the Daltex current market position. The potential profit from the sale of the products is
given in the following table.
Product
Plant Gasoline Kerosene Diesel Jet fuel Asphalt
1 Sh 0.165 --------- Sh 0.140 Sh 0.125 Sh 0.128
2 Sh 0.140 Sh 0.146 Sh 0.126 ------- Sh 0.133
3 -------- Sh 0.139 Sh 0.134 Sh 0.125 Sh 0.130
As indicated in the table, the profit on a product differs at the several plants. In addition, certain
products are not available at all the plants. This is indicated by the dashes .Daltex has the capacity of
70,000 barrels at plant 1;90,000 barrels at plant 2 and 40,000 barrels at plant 3.They have been
requested to supply part or all of the following products:60,000 barrels of gasoline;15,000 barrels of
kerosene;40,000 barrels of diesel fuel;25,000 barrels of asphalt; management wants to schedule
2
production of these products at the three plants with view to maximize the profit. Formulate (and do
not solve) the transportation problem [9 Marks]
b) Briefly describe how you would handle the following situations situation in assignment problem
i) Maximization
ii) Unbalanced problem [6 Marks]
iii) Impossible assignment
c) In general single channel special cases the probability distribution of inter-arrival time of the
customers and the service times are observed to be as under
Interval-arrival service
Time (minutes) Probability Time (minutes) Probability
2 0.5 1 0.1
4 0.3 2 0.3
6 0.1 3 0.25
8 0.1 4 0.25
5 0.10
Using the random numbers given below
For arrivals: 10, 48, 01, 50, 11, 01, 53, 60, 20, 11, 81, and 64
For service: 79, 16, 46, 69, 17, 91, 41, 94, 62, 59, 08, and 62 to simulate the queue for the first 12
arrivals and compute the following:
i) proportion of time the service is idle
ii) The average waiting time of a customer.
iii) The average number waiting in a queue. [15 Marks]
[Total: 30 Marks]
QUESTION TWO
The custom office furniture company is introducing a new line of executive desks made from a
specially selected grade of walnut. Initially, three models – A, B and C
are to be marketed. Each model A desk requires
4
1 1 hours for fabrication,1 hour for assembly, and 1
hour for finishing, each model B desk requires
2
1 1 hours for fabrication,1 hour for assembly and 1 hour
for finishing, each model C desk requires
2
1 1 hours,
4
3 hour, and
2
1 hour for fabrication, assembly, and
finishing, respectively. The profit on each model A desk is Sh 26,the profit on each model B desk is
3
sh28 and the profit on each model C desk is Sh 24.the total time available in the fabrication
department, the assembly department, and the finishing department in the first month of production is
310 hours,205 hours and 190 hours respectively. To maximize the company’s profit, how many desks
of each model should be made in the month? [20 Marks]
QUESTION THREE
A project has the following activities and other characteristics:
activity Preceding
activity
Time estimates in weeks
Most
Optimistic
Most likely Most
Pessimistic
A - 4 7 16
B - 1 5 15
C A 6 12 30
D A 2 5 8
E C 5 11 17
F D 3 6 15
G B 3 9 27
H E,F 1 4 7
I G 4 19 28
Required
a) Draw the PERT network diagram [10 Marks]
b) Identify the critical path [2 Marks]
c) Determine the mean project completion time. [3 Marks]
d) Find the probability that the project is completed in 36 weeks. [5 Marks]
[Total: 20 Marks]
QUESTION FOUR
Three factories supply five ware houses with a particular type of steel. The demand for December from
each of the warehouses and the availability at each factory, together with the transport costs per tonne
are given in the table.
Transport cost Sh per Tonne Tones
To warehouse available
1 2 3 4 5
Factory A 20 27 33 25 34 200
B 22 36 34 28 26 250
C 26 29 27 26 28 300
Tonnes required
100 150 200 100 200
4
REQUIRED
What is the minimum transport cost for December? [20 Marks]
QUESTION FIVE
The human resource manager of a medium sized company decides to recruit two employees S and T in
a particular section of the organization. The section has five fairly defined tasks 1,2,3,4 and 5, and
three employees P, Q and R are already employed in the section. Considering the rather specialized
nature of task 3 and the special qualifications of the recruit S for task 3, the manager decides to assign
task 3 to employee S and then assign the remaining tasks to remaining employees so as to maximize
the total effectiveness. The index of effectiveness of each employee of different task is as under.
Tasks
1 2 3 4 5
Employees P 25 55 60 45 30
Q 45 65 55 35 40
R 10 35 45 55 65
S 40 30 70 40 60
T 55 45 40 55 10
Assign the tasks for maximizing total effectiveness. Critically examine whether the decision of the
manager to assign task 3 to employees was correct. [20 Marks]
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