S.Y.MCA (Part II) (Under Faculty of Engg.) Examination, 2017
OPERATIONS RESEARCH
Day and Date Monday, 8-5-2017 Total Marks 100
Time: 3.00 p.m. to 6.00 p.m.
Instructions All questions are compulsory.
Use of scientific calculator allowed.
1. Choose the correct alternative 20
Operations Research uses models to help the management to determine its
scientifically.
Policies Actions
Both a and b None of the above
Operations Research is a
Science Art
Mathematics Both a and b
What have been constructed for Operations Research problems and methods
for solving the models that are available in many cases
Scientific Models Algorithms
Mathematical Models None of the above
What aims at optimizing inventory levels
Inventory control Inventory capacity
Inventory planning None of the above
Which theory concerns making sound decisions under conditions of certainty,
risk and uncertainty
Game Theory Network Analysis
Decision Theory None of the above
Seat
No.
P.T.O.
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To find the optimal solution, we apply
LPP VAM
MODI Method Rim
Who defined Operations Research as scientific method of providing executive
departments with a quantitative basis for decisions regarding the operations
under their control
Morse and Kimball (1946) P.M.S. Blackett (1948)
E.L. Arnoff and M.J. Netzorg None of the above
Who defined Operations Research as scientific approach to problem solving
for executive management
E.L. Arnoff P.M.S. Blackett
H.M. Wagner None of the above
Who defined Operations Research as an aid for the executive in marketing
his decisions by providing him with the quantitative information based on
the scientific method of analysis
C. Kitte H.M. Wagner
E.L. Arnoff None of the above
10) Operations Research has the characteristics that it is done by a team
of
Scientists Mathematicians
Academics All of the above
11) There is a great scope for working as a team to solve
problems of defence by using the Operations Research approach.
Economists Administrators
Statisticians and Technicians All of the above
12) Operations Research cannot give perfect to problems.
Answers Solutions
Both a and b Decisions
13) Operations Research simply helps in improving the of the
solution but does not result in a perfect solution.
Quality Clarity
Look None of the above
14) Operations Research involves attack of complex problems to
arrive at the optimum solution.
Scientific Systematic
Both a and b Statistical
15) A solution may be extracted from a model either by
Conducting experiments on it Mathematical analysis
Both a and b Diversified Techniques
16) Operations Research which is a very powerful tool for
Research Decision Making
Operations None of the above
17) Who coined the term Operations Research
J. F. McCloskey F.N. Trefethen
P.F. Adams Both a and b
18) The term Operations Research was coined in the year
1950 1940
1978 1960
19) This innovative science of Operations Research was discovered during
Civil War World War I
World War II Industrial Revolution
20) Operations Research was known as an ability to win a war without really
going into a
Battle field Fighting
War Both a and b
2. Attempt any four
A road transport company has one reservation clerk on duty at a time. She
handles information of bus schedules and marks reservation customer arrive
at a rate of 8 per hour and clerk can serve 12 customers on an average per
hour. After stating your assumption, answer the following.
What is the average number of customer waiting for service for the clerk
ii) What is the average time a customer has to wait before getting service
Solve the following assignment problem
Solve the L.P.P by Simplex method
Max. Z 5x1 5x2 subject to
3x1 5x2 15
5x1 2x2 10
x1, x2
Solve the following game
People arrive at a theater both in a poisson distributed arrival rate of 25 per hr.
service time is constant at 2 minutes. Calculate
The mean number in the waiting time
ii) The mean waiting time.
SECTION I
3. Attempt any one 10
Solve the integer programming problem using Gomory's cutting plane method.
Maximize Z x1 4x2 Subject to
2x1 4x2 7
5x1 3x2 15
x1, x2 and integer.
Solve transportation problem
4. Obtain the optimal solution for the following transportation problem. 10
D1 D2 D3 Supply
S1 3 8 5 5
S2 4 4 2 8
S3 6 5 8 7
S4 2 7 3 14
Demand 7 9 18
Required 5 8 3 10
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SECTION II
5. Attempt any four
Describe the steps for processing n jobs through two machines.
A shop is about to order heaters for a forecast spell of cold weather. The shop
pays Rs. 1,000 for each heater and during the cold spell, they sell for Rs. 2,000
each. The demand for the heater declines after the cold spell is over and any
unsold units are sold at Rs. 500. Previous experience suggests the likely
demand for heaters is follows
Demand 10 20 30 40 50
Probability 0.20 0.30 0.30 0.10 0.10
How many heaters should the shop buy
A project has the following time scheduling activity.
Activity 1 −2 1 − 3 1 − 4 2 − 5 3 − 6 3 −7 4 − 6 5 − 8 6 − 9 7 − 8 8 − 9
Duration 2 2 1 4 8 5 3 1 5 4 3
Construct PERT network and compute critical path and its duration.
Find the EOQ for the following data
Annual usage 1000 pieces
Cost per pieces Rs. 200
Ordering cost Rs. 6/order
Expediting cost Rs. 4/order
Inventory holding cost 20% of avg. inventory
Material holding cost Rs. 1 per piece.
A contractor has to supply 10,000 bearings/day to an automobile manufacturer.
He finds that, when he starts a production run, he can produce 25,000 bearing
per day. The cost of holding a bearing in stock for one year is 20 paise and
set-up cost of a production run is Rs. 180.00. How frequently should production
run be made
6. Attempt the following
Consider the following data . 10
Unit cost Rs. 100, Order cost Rs. 160, Inventory carry cost Rs. 20.
Back-order cost or stock-out cost Rs. 10. Annual Demand 1000 Unit.
Compute the following
Mini cost Order quantity
ii) Time between orders
iii) Maximum inventory level.
Consider a project consisting of the following jobs 10
Job Predecessor Days
A 15
B 10
C B 10
D B 10
E B 5
F E 5
G F 20
H E 10
I H 15
OR
Describe steps to process n-jobs through two machines. 10