Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 6th Sem New 2163201 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2163201 Date:10/05/2019
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 the advantages of Model Building in Operations research. 03
(b) Use simplex method to maximize ?? = 4?? 1
+ 3?? 2
Subject to constraints
2?? 1
+ ?? 2
? 1000, ?? 1
+ ?? 2
? 800, ?? 1
? 400, ?? 2
? 700, ?? 1
, ?? 2
? 0
04
(c) What are the features of Operations research approach? Discuss in brief. 07
Q.2 (a) Solve the following LPP graphically
Minimize ?? = 600?? + 400??
Subject to 3?? + 3?? ? 40, 3?? + ?? ? 40, 2?? + 5?? ? 44, ?? , ?? ? 0
03
(b) Explain the primal ? dual relationship. 04
(c) Maximize ?? = 2?? 1
+ 3?? 2
+ 4?? 3
Subject to constraints
3?? 1
+ ?? 2
+ 4?? 3
? 600, 2?? 1
+ 4?? 2
+ 2?? 3
? 480,
2?? 1
+ 3?? 2
+ 3?? 3
= 540, ?? 1
, ?? 2
, ?? 3
? 0
07
OR
(c) Use Two phase method to solve the following LPP
???????????????? ?? = ?? 1
+ ?? 2
Subject to the constraints
2?? 1
+ ?? 2
? 4, ?? 1
+ 7?? 2
? 7, ?? 1
, ?? 2
? 0
07
Q.3 (a) Give an algorithm for solving a transportation problem. 03
(b) Solve the following Assignment problem
I II III IV V
A 10 5 13 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
04
(c)
Solve the transportation problem (find initial basic solution with VAM and
Optimal Solution using MODI method)
To D1 D2 D3 D4 Supply
From
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14
07
OR
Q.3 (a) How would you solve the assignment problem where the objective
function is of maximization type?
03
(b) Explain Degeneracy in Transportation problem and its resolution. 04
(c) A manufacturer wants to ship 22 loads of his product as shown below.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2163201 Date:10/05/2019
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 the advantages of Model Building in Operations research. 03
(b) Use simplex method to maximize ?? = 4?? 1
+ 3?? 2
Subject to constraints
2?? 1
+ ?? 2
? 1000, ?? 1
+ ?? 2
? 800, ?? 1
? 400, ?? 2
? 700, ?? 1
, ?? 2
? 0
04
(c) What are the features of Operations research approach? Discuss in brief. 07
Q.2 (a) Solve the following LPP graphically
Minimize ?? = 600?? + 400??
Subject to 3?? + 3?? ? 40, 3?? + ?? ? 40, 2?? + 5?? ? 44, ?? , ?? ? 0
03
(b) Explain the primal ? dual relationship. 04
(c) Maximize ?? = 2?? 1
+ 3?? 2
+ 4?? 3
Subject to constraints
3?? 1
+ ?? 2
+ 4?? 3
? 600, 2?? 1
+ 4?? 2
+ 2?? 3
? 480,
2?? 1
+ 3?? 2
+ 3?? 3
= 540, ?? 1
, ?? 2
, ?? 3
? 0
07
OR
(c) Use Two phase method to solve the following LPP
???????????????? ?? = ?? 1
+ ?? 2
Subject to the constraints
2?? 1
+ ?? 2
? 4, ?? 1
+ 7?? 2
? 7, ?? 1
, ?? 2
? 0
07
Q.3 (a) Give an algorithm for solving a transportation problem. 03
(b) Solve the following Assignment problem
I II III IV V
A 10 5 13 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
04
(c)
Solve the transportation problem (find initial basic solution with VAM and
Optimal Solution using MODI method)
To D1 D2 D3 D4 Supply
From
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14
07
OR
Q.3 (a) How would you solve the assignment problem where the objective
function is of maximization type?
03
(b) Explain Degeneracy in Transportation problem and its resolution. 04
(c) A manufacturer wants to ship 22 loads of his product as shown below.
07
2
The shipping cost is Rs. 10 per load per km. What shipping schedule
should be used in order to minimize the total transportation cost?
[Use VAM to find the initial basic feasible solution and MODI method
for Optimal solution]
D1 D2 D3 D4 D5 Supply
S1 5 8 6 6 3 8
S2 4 7 7 6 5 5
S3 8 4 6 6 4 9
Demand 4 4 5 4 8 25 / 22
Q.4 (a) Draw the network diagram for following
Activity A B C D E F G H
Pre.
Activity
- A A B B, C E D, F G
03
(b) What is critical activity in network diagram? What is the importance of
critical path in any project?
04
(c) Information on the activities required for a project is as follows:
Activity
Name
A B C D E F G H I J K
Activity
Node
1-2 1-3 1-4 2-5 3-5 3-6 3-7 4-6 5-7 6-8 7-8
Duration
(Days)
2 7 8 3 6 10 4 6 2 5 6
Find total float, free float and independent float for each activity.
07
OR
Q.4 (a) Define Reneging, Balking and Jockeying in Queuing System. 03
(b) A TV repairman finds that the time spent on his job has an exponential
distribution with a mean of 30 minutes. If he repairs the sets in order in
which they came in, and if the arrival rate of sets follows a poisson
distribution with an average rate of 10 per 8-hour a day, what is the
repairman?s expected idle time each day? Find the expected number of
TV sets in the system.
04
(c) The data on the running costs per year and resale price of equipment A,
whose price is Rs. 2,00,000 are as follows.
Year 1 2 3 4 5 6 7
Running
cost
30000 38000 46000 58000 72000 90000 110000
Resale
value
100000 50000 25000 12000 8000 8000 8000
What is the optimum period of replacement?
07
Q.5 (a) What is Random number? 03
(b) What are the advantages of Simulation? 04
(c) The following mortality rates have been observed for certain type of fuse:
Week 1 2 3 4 5
% failing
by the
end of
week
5 15 35 57 100
There are 1000 fuses in use and it costs Rs. 5 to replace an individual
fuse. If all fuses were replaced simultaneously it would cost Rs. 1.25 per
fuse. What is the optimal replacement plan?
07
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2163201 Date:10/05/2019
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 the advantages of Model Building in Operations research. 03
(b) Use simplex method to maximize ?? = 4?? 1
+ 3?? 2
Subject to constraints
2?? 1
+ ?? 2
? 1000, ?? 1
+ ?? 2
? 800, ?? 1
? 400, ?? 2
? 700, ?? 1
, ?? 2
? 0
04
(c) What are the features of Operations research approach? Discuss in brief. 07
Q.2 (a) Solve the following LPP graphically
Minimize ?? = 600?? + 400??
Subject to 3?? + 3?? ? 40, 3?? + ?? ? 40, 2?? + 5?? ? 44, ?? , ?? ? 0
03
(b) Explain the primal ? dual relationship. 04
(c) Maximize ?? = 2?? 1
+ 3?? 2
+ 4?? 3
Subject to constraints
3?? 1
+ ?? 2
+ 4?? 3
? 600, 2?? 1
+ 4?? 2
+ 2?? 3
? 480,
2?? 1
+ 3?? 2
+ 3?? 3
= 540, ?? 1
, ?? 2
, ?? 3
? 0
07
OR
(c) Use Two phase method to solve the following LPP
???????????????? ?? = ?? 1
+ ?? 2
Subject to the constraints
2?? 1
+ ?? 2
? 4, ?? 1
+ 7?? 2
? 7, ?? 1
, ?? 2
? 0
07
Q.3 (a) Give an algorithm for solving a transportation problem. 03
(b) Solve the following Assignment problem
I II III IV V
A 10 5 13 15 16
B 3 9 18 13 6
C 10 7 2 2 2
D 7 11 9 7 12
E 7 9 10 4 12
04
(c)
Solve the transportation problem (find initial basic solution with VAM and
Optimal Solution using MODI method)
To D1 D2 D3 D4 Supply
From
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14
07
OR
Q.3 (a) How would you solve the assignment problem where the objective
function is of maximization type?
03
(b) Explain Degeneracy in Transportation problem and its resolution. 04
(c) A manufacturer wants to ship 22 loads of his product as shown below.
07
2
The shipping cost is Rs. 10 per load per km. What shipping schedule
should be used in order to minimize the total transportation cost?
[Use VAM to find the initial basic feasible solution and MODI method
for Optimal solution]
D1 D2 D3 D4 D5 Supply
S1 5 8 6 6 3 8
S2 4 7 7 6 5 5
S3 8 4 6 6 4 9
Demand 4 4 5 4 8 25 / 22
Q.4 (a) Draw the network diagram for following
Activity A B C D E F G H
Pre.
Activity
- A A B B, C E D, F G
03
(b) What is critical activity in network diagram? What is the importance of
critical path in any project?
04
(c) Information on the activities required for a project is as follows:
Activity
Name
A B C D E F G H I J K
Activity
Node
1-2 1-3 1-4 2-5 3-5 3-6 3-7 4-6 5-7 6-8 7-8
Duration
(Days)
2 7 8 3 6 10 4 6 2 5 6
Find total float, free float and independent float for each activity.
07
OR
Q.4 (a) Define Reneging, Balking and Jockeying in Queuing System. 03
(b) A TV repairman finds that the time spent on his job has an exponential
distribution with a mean of 30 minutes. If he repairs the sets in order in
which they came in, and if the arrival rate of sets follows a poisson
distribution with an average rate of 10 per 8-hour a day, what is the
repairman?s expected idle time each day? Find the expected number of
TV sets in the system.
04
(c) The data on the running costs per year and resale price of equipment A,
whose price is Rs. 2,00,000 are as follows.
Year 1 2 3 4 5 6 7
Running
cost
30000 38000 46000 58000 72000 90000 110000
Resale
value
100000 50000 25000 12000 8000 8000 8000
What is the optimum period of replacement?
07
Q.5 (a) What is Random number? 03
(b) What are the advantages of Simulation? 04
(c) The following mortality rates have been observed for certain type of fuse:
Week 1 2 3 4 5
% failing
by the
end of
week
5 15 35 57 100
There are 1000 fuses in use and it costs Rs. 5 to replace an individual
fuse. If all fuses were replaced simultaneously it would cost Rs. 1.25 per
fuse. What is the optimal replacement plan?
07
3
OR
Q.5 (a) Define Simulation. Enlist the types of simulation. 03
(b) Explain the Group replacement policy versus Individual replacement
policy.
04
(c) A company trading in motor vehicle spare parts wishes to determine the
levels of stock it should carry for the items in its range. The demand is not
certain and there is a lead time for stock replenishment. For an item A,
the following information is obtained;
Demand
(units/day
3 4 5 6 7
Probability 0.1 0.2 0.3 0.3 0.1
Carrying cost: Rs. 2 /unit/ day
Ordering cost: Rs. 50/ oder
Lead time for replenishment: 3 days
Stock on hand at the beginning of simulation process was 20 units
Carry out the simulation over a period of 10 days with the objective of
evaluating the inventory rule: Oder 15 units when present inventory plus
any outstanding oder falls below 15 units.
Random number: 0, 9, 1, 1, 5, 1, 8, 6, 3, 5
Your calculation should include the total cost of operating inventory rule
for 10 days.
07
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This post was last modified on 20 February 2020