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ST. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – OCTOBER 2013
BBM – V SEMESTER
OPERATIONS RESEARCH
Duration: 3 HOURS Max. Marks: 100
SECTION – A
I. Answer ALL the following questions. (2 marks each) (10×2=20)
1. “Operations Research is a scientific and systematic problem solving tool in every field”-
with reference to this statement bring out the Interdisciplinary feature of operations
research.
2. Introduce suitable variables for the following expressions:
a. 2x+3y=20 b. 4a+5b >= 6 c. 20p+30q<= 55 d. 7x+4y >=10
3. State any four techniques of Operations Research.
4. What is the coefficient introduced inthe objective function in case of slack and surplus
variables? Give an example.
5. For the given equation 2x + 3y <= 6 plot and identify where the feasible region lies.
6. Explain Unbalanced Assignment Problem.
7. Mention the three techniques of finding the Initial Basic Feasible Solution.
8. Define utility in decision theory.
9. Show with help of a diagram Head Event and Tail Event for an activity.
10. In case of Transportation problem, what is meant by degeneracy and non- degeneracy
solution.
SECTION – B
II. Answer ANY FOUR of the following questions (4×5= 20)
11. An Electric Appliance Company produces two products: Refrigerators and Ranges.
Production takes place in two separate departments I and II. Refrigerators are produced
in department I and Ranges in department II. The company’s two products are sold on a
weekly basis. The weekly production cannot exceed 25 Refrigerators and 35 Ranges. The
company regularly employs a total of 60 workers in the two departments. A Refrigerator
requires 2 man-weeks labour while a Range requires 1 man-week labour. A Refrigerator
contributes a profit of Rs. 60 and a Range contributes a profit of Rs. 40. How many units
of refrigerators and ranges should the company produce to realize the maximum profit?
Formulate the above as an LPP.
12. “O.R. is the application of scientific methods to problem arising from operations
involving integrated system of men, machines and materials.”—with reference to this
bring out the various features of Operations Research.
13. Obtain the Primal and Dual of the following LPP and state how many constraints and
variables are formed after duality.
Max Z = 3x + 4y + 2z
Subject to constraints:
2
x + y <= 8
y + z <= 15
8x + 2y <= 2
x + y – z <= 12
2x + 2y + z <= 22
4x + 3y <= 21
z <= 3
Where x, y, z >= 0
14. International Oil Company has three Refineries and four Depots. Transportation costs
per ton and requirements are given below:
D1 D2 D3 D4 Capacity
P1 5 7 13 10 700
P2 8 6 14 13 500
P3 12 10 9 11 800
Requirement 300 600 700 400 ?
Determine the Initial Basic feasible Solution using NWCM.
15. The following represents the various activities of a project:
Activity Preceding Activity
A —
B —
C A
D A
E B
F C
G D,E
Draw a network diagram for the above and show the activities after numbering the events.
16. “Decision- maker is a person who is responsible for making decisions. Decisions are
made under various situations”— In this context, explain the various decision – making
environments.
SECTION – C
III. Answer ANY THREE of the following questions (3×15=45)
17. By using the graphical method solve the following LPP:
Max Z = 3a + 4b
Subject to constraints:
5a + 4b <= 200
3a + 5b <= 150
5a + 4b >= 100
8a + 4b >= 80
Where, a, b >= 0. Also show the necessary verification workings.
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18. Solve the following LPP using Simplex Method:
Max Z = 3x + 2y + 5z
Subject to constraints:
x + 2y + z <= 430
3x + 2z <= 460
x + 4y <= 420
Non – Negativity Restriction = x, y, z >= 0
19. The owner of a small machine shop has four mechanics available to assign jobs for the
day. Five jobs offered with expected profit for each mechanic on each jobs, which are as
follows:
Mechanics \ Jobs A B C D E
M1 62 78 50 111 82
M2 71 84 61 73 59
M3 87 92 111 72 81
M4 48 64 87 77 80
By using the Hungarian Method, find the assignment of mechanics to the job that will
result in Maximum Profit. Which job should be declined?
20. (a)“A model is a representation of the reality. Most of our thinking of operation research
in business take place in the context of models”— with reference to this statement briefly
explain the various types of models used in operations research. (10 marks)
(b) Write a short note on Decision Tree Analysis (5marks)
21. Solve the following Transportation Problem using VAM to arrive at the IBFS and also
TEST IT FOR OPTIMALITY using MODI method.
From\ To I II III IV SUPPLY
A 15 10 17 18 2
B 16 13 12 13 6
C 12 17 20 11 7
DEMAND 3 3 4 5 ?
SECTION -D
IV. Answer the following question (COMPULSORY) (1×15=15)
22. St. Joseph’s College of Commerce Final year BBM students had taken up a project work
in the field of construction. BBM students of SJCC were known for their creativity and
were also very confident in taking up the project because they had studied Operations
Research as one of the subjects. The project was to be completed within a stipulated
period of time. Lot of pressures were put on the students as there were in their final year.
They divided the entire project into different activities and events so that they could
reduce their project duration and complete on time. The following were the details of the
project:
4
ACTIVITY to (weeks) tm (weeks) tp (weeks)
1-2 1 1 7
1-3 1 4 7
1-4 2 2 8
2-5 1 1 1
3-5 2 5 14
4-6 2 5 8
5-6 3 6 15
With the details available keeping in mind you are one among the final year BBM student,
present the Network Project Report Plan using the Network Analysis techniques for the
following:
a. Draw the project network.
b. Determine the Expected Project Length and identify all the paths.
c. Show Early Start, Early Finish, Late Start, and Late Finish time of the project and
Total Float.
d. Compute the variance and standard deviation of the project.
e. What is the probability that the project will be completed within 19 weeks?
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