GTU BE 6th Semester 2163201 Operation Research Summer 2018 Question Paper

Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018
Subject Code: 2163201 Date: 28/04/2018
Subject Name: Operation Research
Time: 10:30 AM to 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS
Q.1 (a) Discuss in brief the areas of application of Operation Research. 03
(b)Use simplex method to solve following LPP
???????????????? ?? = 45?? 1
+ 80?? 2
Subject to the constraints
5?? 1
+ 20?? 2
= 400, 10?? 1
+ 15?? 2
= 450, ?? 1
, ?? 2
= 0

04
(c)Explain the Phases of OR study.
07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03
(b) Solve the following LPP using graphical method.
???????????????? ?? = 4?? + 5??
Subject to the constraints
?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0
04
(c) Solve the following LPP using Two phase method.
???????????????? ?? = 60?? 1
+ 48?? 2
Subject to the constraints
4?? 1
+ 2?? 2
= 8, 2?? 1
– 4?? 2
= 6, ?? 1
, ?? 2
= 0
07
OR
(c) Solve the following LPP using BIG ? M method.
???????????????? ?? = 40?? 1
+ 20?? 2
Subject to the constraints
2?? 1
+ 5?? 2
= 48, 8?? 1
+ 5?? 2
= 72, ?? 1
, ?? 2
= 0
07
Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.
Give its advantage and disadvantage.
03
(b) A company has three plants at location A, B and C which produce the same
product. It has to supply this to buyers located at P, Q and R. The weekly plant
capacities for A, B and C are 250, 800 and 350 units respectively, while the
buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit
shipping costs (in Rs) are given as:
Plant
Buyers
P Q R
A 8 4 10
B 9 7 9
C 6 5 8
Determine the distribution for the company so as to minimize the cost of
transportation using Least Cost Method.
04
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018
Subject Code: 2163201 Date: 28/04/2018
Subject Name: Operation Research
Time: 10:30 AM to 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS
Q.1 (a) Discuss in brief the areas of application of Operation Research. 03
(b)Use simplex method to solve following LPP
???????????????? ?? = 45?? 1
+ 80?? 2
Subject to the constraints
5?? 1
+ 20?? 2
= 400, 10?? 1
+ 15?? 2
= 450, ?? 1
, ?? 2
= 0

04
(c)Explain the Phases of OR study.
07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03
(b) Solve the following LPP using graphical method.
???????????????? ?? = 4?? + 5??
Subject to the constraints
?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0
04
(c) Solve the following LPP using Two phase method.
???????????????? ?? = 60?? 1
+ 48?? 2
Subject to the constraints
4?? 1
+ 2?? 2
= 8, 2?? 1
– 4?? 2
= 6, ?? 1
, ?? 2
= 0
07
OR
(c) Solve the following LPP using BIG ? M method.
???????????????? ?? = 40?? 1
+ 20?? 2
Subject to the constraints
2?? 1
+ 5?? 2
= 48, 8?? 1
+ 5?? 2
= 72, ?? 1
, ?? 2
= 0
07
Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.
Give its advantage and disadvantage.
03
(b) A company has three plants at location A, B and C which produce the same
product. It has to supply this to buyers located at P, Q and R. The weekly plant
capacities for A, B and C are 250, 800 and 350 units respectively, while the
buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit
shipping costs (in Rs) are given as:
Plant
Buyers
P Q R
A 8 4 10
B 9 7 9
C 6 5 8
Determine the distribution for the company so as to minimize the cost of
transportation using Least Cost Method.
04
(c) ABC company is engaged in manufacturing 5 brands of packed snacks. It has
five manufacturing setups, each capable of manufacturing any of its brands one
at a time, The costs to make a brand on these setups vary according to
following table.
S1 S2 S3 S4 S5
B1 4 6 7 5 15
B2 7 3 6 9 5
B3 8 5 4 6 9
B4 9 12 7 11 10
B5 7 5 9 8 11
Find the optimum assignment on these setups resulting in the minimum cost?
07
OR
Q.3 (a) Classify the Assignment problem in detail. 03
(b) Solve the following transportation problem using Vogel?s Approximation
Method.
To D1 D2 D3 D4 Available
Units From
F1 10 9 11 10 200
F2 12 10 8 7 60
F3 8 9 11 12 40
Demand 100 50 60 40
[D stands for destination. F stands for factory.]
04
(c) Define the simulation model. Distinguish between deterministic and stochastic
simulation mode.
07
Q.4 (a) Discuss the differences between CPM and PERT. 03
(b) What is critical path? State the necessary and sufficient condition of critical path.
Can a project have multiple critical paths?
04
(c) Determine the critical path for the following network. What is the total time
required for the project. Also find the free float and independent float for each
activity.
Activity 1-2 1-3 2-4 3-4 3-5 4-6 5-6
Duration 2 8 4 1 2 5 6
07
OR
Q.4 (a) Enlist the components of the Queuing System. Define Balking in Queuing
System.
03
(b) What do you mean by Minimum Spanning Tree? Discuss any algorithm for
finding minimum spanning tree.
04
(c) A researcher studying the ?Q? theory at a counter of a railway station has
concluded that the inter-arrival rate at a desk is 3 minutes while the inter-
service, both following Poisson distribution, is 2 minutes. Answer the
following questions using the given facts.
1) What is the average waiting time of a customer in the system?
2) How many customers are there waiting in the queue?
3) The management is ready to start a new counter if the average waiting time
in the system is 8 minutes; find the arrival rate (per hour) of the customers.
07
Q.5 (a) Explain Individual replacement versus group replacement. 03
(b) Determine the age at which the following type of machine be replaced:
Cost price = Rs 8,000
Operating Costs = Rs 1000 for the first Year, increasing by Rs 500 every year
Resale Value = Rs 4000 for first year, decreasing by Rs 500 every year.
04
(c) A company manufactures around 200 mopeds. Depending upon the
availability of raw materials and other conditions, the daily production has
07
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018
Subject Code: 2163201 Date: 28/04/2018
Subject Name: Operation Research
Time: 10:30 AM to 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS
Q.1 (a) Discuss in brief the areas of application of Operation Research. 03
(b)Use simplex method to solve following LPP
???????????????? ?? = 45?? 1
+ 80?? 2
Subject to the constraints
5?? 1
+ 20?? 2
= 400, 10?? 1
+ 15?? 2
= 450, ?? 1
, ?? 2
= 0

04
(c)Explain the Phases of OR study.
07

Q.2 (a) What is the degeneracy in simplex method? How it can be resolved? 03
(b) Solve the following LPP using graphical method.
???????????????? ?? = 4?? + 5??
Subject to the constraints
?? + ?? = 1, ?? + 2?? = 4, ?? = 4, ?? = 4, ?? , ?? = 0
04
(c) Solve the following LPP using Two phase method.
???????????????? ?? = 60?? 1
+ 48?? 2
Subject to the constraints
4?? 1
+ 2?? 2
= 8, 2?? 1
– 4?? 2
= 6, ?? 1
, ?? 2
= 0
07
OR
(c) Solve the following LPP using BIG ? M method.
???????????????? ?? = 40?? 1
+ 20?? 2
Subject to the constraints
2?? 1
+ 5?? 2
= 48, 8?? 1
+ 5?? 2
= 72, ?? 1
, ?? 2
= 0
07
Q.3 (a) Discuss the Northwest and Least cost method for finding initial basic solution.
Give its advantage and disadvantage.
03
(b) A company has three plants at location A, B and C which produce the same
product. It has to supply this to buyers located at P, Q and R. The weekly plant
capacities for A, B and C are 250, 800 and 350 units respectively, while the
buyer requirements are 700, 200 and 500 for P, Q and R respectively. The unit
shipping costs (in Rs) are given as:
Plant
Buyers
P Q R
A 8 4 10
B 9 7 9
C 6 5 8
Determine the distribution for the company so as to minimize the cost of
transportation using Least Cost Method.
04
(c) ABC company is engaged in manufacturing 5 brands of packed snacks. It has
five manufacturing setups, each capable of manufacturing any of its brands one
at a time, The costs to make a brand on these setups vary according to
following table.
S1 S2 S3 S4 S5
B1 4 6 7 5 15
B2 7 3 6 9 5
B3 8 5 4 6 9
B4 9 12 7 11 10
B5 7 5 9 8 11
Find the optimum assignment on these setups resulting in the minimum cost?
07
OR
Q.3 (a) Classify the Assignment problem in detail. 03
(b) Solve the following transportation problem using Vogel?s Approximation
Method.
To D1 D2 D3 D4 Available
Units From
F1 10 9 11 10 200
F2 12 10 8 7 60
F3 8 9 11 12 40
Demand 100 50 60 40
[D stands for destination. F stands for factory.]
04
(c) Define the simulation model. Distinguish between deterministic and stochastic
simulation mode.
07
Q.4 (a) Discuss the differences between CPM and PERT. 03
(b) What is critical path? State the necessary and sufficient condition of critical path.
Can a project have multiple critical paths?
04
(c) Determine the critical path for the following network. What is the total time
required for the project. Also find the free float and independent float for each
activity.
Activity 1-2 1-3 2-4 3-4 3-5 4-6 5-6
Duration 2 8 4 1 2 5 6
07
OR
Q.4 (a) Enlist the components of the Queuing System. Define Balking in Queuing
System.
03
(b) What do you mean by Minimum Spanning Tree? Discuss any algorithm for
finding minimum spanning tree.
04
(c) A researcher studying the ?Q? theory at a counter of a railway station has
concluded that the inter-arrival rate at a desk is 3 minutes while the inter-
service, both following Poisson distribution, is 2 minutes. Answer the
following questions using the given facts.
1) What is the average waiting time of a customer in the system?
2) How many customers are there waiting in the queue?
3) The management is ready to start a new counter if the average waiting time
in the system is 8 minutes; find the arrival rate (per hour) of the customers.
07
Q.5 (a) Explain Individual replacement versus group replacement. 03
(b) Determine the age at which the following type of machine be replaced:
Cost price = Rs 8,000
Operating Costs = Rs 1000 for the first Year, increasing by Rs 500 every year
Resale Value = Rs 4000 for first year, decreasing by Rs 500 every year.
04
(c) A company manufactures around 200 mopeds. Depending upon the
availability of raw materials and other conditions, the daily production has
07
been varying from 196 mopeds to 204 mopeds, whose probability is as given
below:
Production(Per
day)196 197 198 199 200 201 202 203 204
Probability 0.05 0.09 0.12 0.14 0.20 0.15 0.11 0.08 0.06
The finished mopeds are transported in 3-storyed lorry that can accommodate
only 200 mopeds. Use the following random numbers: 82, 89, 78, 24, 53, 61,
18, 45, 4, 23, 50, 77, 27, 54, 10. Simulate the mopeds waiting in the factory for
next 15 days.
1. What will be the average no. of mopeds waiting in the factory?
2. What will be the average no. of empty spaces in the lorry?
OR
Q.5 (a)What is simulation? What are the advantages and limitations of simulation?
03
(b) What is replacement problem? Describe some important replacement situations
and policies.
04
(c)A toll booth owner is presently using a manual system having service rate of 10
vehicles per minutes. On an average 8 vehicles are coming in minute. Calculate:
1. Utilization factor of booth operator
2. Idle time for booth operator in a day having working hour of 8 hours
3. Number of persons waiting in the system
4. Number of persons waiting in the queue
5. Average waiting time in the queue
07

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