Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 7th Sem New 2171901 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2171901 Date: 28/11/2019
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) Define Operations research. Explain any two area of feasible
application of OR in your college.
03
(b) Briefly explain: Phases of Operation Research. 04
(c) Tom has received certain amount as will from his maternal parents.
He is contemplating how much money he should invest in various
alternatives open to him so as to maximize return on investment. The
investment alternatives are given below with his subjective estimate
of the risk involved on a five ? point scale. He decided that the risk
should not be more than 4 and the fund should not be locked up for
more than 15 years. He would necessarily invest at least 25% in house
construction. Formulate the LPP:
Alternatives Return No. of
Years
Risk
Govt. Securities 6 15 1
Company deposits 13 3 3
Time deposits 10 5 2
Equity Shares 20 6 5
Construction
business
25 10 1
07
Q.2 (a) What are the characteristics of Linear Programming Problems?
Discuss.
03
(b) Solve problem using graphical method:
Max Z = 20 x1 + 30 x2
Subject to 2x1 + 3x2 ? 120
x1 + x2 ? 40
2x1 + 1.5x2 ? 90
x1, x2 ? 0
04
(c) Solve the following problem using simplex method:
Minimize Z = x1 ? 3x2 + 2x3
Subject to 3x1 ? x2 + 2x3 ? 7
-2x1 + 4x2 + 2x3 ? 12
-4x1 + 3x2 + 8x3 ? 10
x1, x2, x3 ? 0
07
OR
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2171901 Date: 28/11/2019
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) Define Operations research. Explain any two area of feasible
application of OR in your college.
03
(b) Briefly explain: Phases of Operation Research. 04
(c) Tom has received certain amount as will from his maternal parents.
He is contemplating how much money he should invest in various
alternatives open to him so as to maximize return on investment. The
investment alternatives are given below with his subjective estimate
of the risk involved on a five ? point scale. He decided that the risk
should not be more than 4 and the fund should not be locked up for
more than 15 years. He would necessarily invest at least 25% in house
construction. Formulate the LPP:
Alternatives Return No. of
Years
Risk
Govt. Securities 6 15 1
Company deposits 13 3 3
Time deposits 10 5 2
Equity Shares 20 6 5
Construction
business
25 10 1
07
Q.2 (a) What are the characteristics of Linear Programming Problems?
Discuss.
03
(b) Solve problem using graphical method:
Max Z = 20 x1 + 30 x2
Subject to 2x1 + 3x2 ? 120
x1 + x2 ? 40
2x1 + 1.5x2 ? 90
x1, x2 ? 0
04
(c) Solve the following problem using simplex method:
Minimize Z = x1 ? 3x2 + 2x3
Subject to 3x1 ? x2 + 2x3 ? 7
-2x1 + 4x2 + 2x3 ? 12
-4x1 + 3x2 + 8x3 ? 10
x1, x2, x3 ? 0
07
OR
2
(c) Develop dual problem and solve the same:
Max Z = 40 x1 + 50 x2
Subject to 2x1 + 3x2 ? 3
8x1 + 4x2 ? 5
x1, x2 ? 0
Also, find out the result of primal from final table of dual.
07
Q.3 (a) How profit maximization problem can be solved by assignment
Problem?
03
(b) A bank has only one cashier. Cashier working style follows Poisson
distribution with mean service rate of 8 customer per hour. The
customer arrives at a rate of 5 per hour during entire 8 hours. Find
out:
i. Equipment utilization
ii. The percentage time that an arriving customer has to wait.
iii. Average system time.
04
(c) Solve the minimal assignment problem whose matrix as follows:
Also find the other optimal solution, if any.
1 2 3 4
I 2 3 4 5
II 4 5 6 7
III 7 8 9 8
IV 3 5 8 4
07
OR
Q.3 (a) How to tackle the non-square matrix in the assignment problem?
Explain with suitable example.
03
(b) Explain: Kendell?s Notation in terms of Queuing Theory 04
(c) Find out the optimum transportation cost based on given table:
1 2 3 4
Supply
A 4 6 8 13 50
B 13 11 10 8 70
C 14 4 10 13 30
D 9 11 13 8 50
Demand ? 25 35 105 20
07
Q.4 (a) Explain: Procedure for Group Replacement Theory 03
(b) Derive the equation for Economic Order Quantity (EOQ) for constant
demand with the condition of no shortage.
04
(c) The initial price of an equilibrium is Rs. 5000. The running cost varies
as below:
Year 1 2 3 4 5 6 7
Running
Cost
400 500 700 1000 1300 1700 2100
Taking a discount rate of 0.90, find out the optimum replacement
interval.
07
OR
Q.4 (a) Discuss different types of costs associated with inventory. 03
(b) Explain: ABC analysis and its importance. 04
FirstRanker.com - FirstRanker's Choice
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VII (New) EXAMINATION ? WINTER 2019
Subject Code: 2171901 Date: 28/11/2019
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) Define Operations research. Explain any two area of feasible
application of OR in your college.
03
(b) Briefly explain: Phases of Operation Research. 04
(c) Tom has received certain amount as will from his maternal parents.
He is contemplating how much money he should invest in various
alternatives open to him so as to maximize return on investment. The
investment alternatives are given below with his subjective estimate
of the risk involved on a five ? point scale. He decided that the risk
should not be more than 4 and the fund should not be locked up for
more than 15 years. He would necessarily invest at least 25% in house
construction. Formulate the LPP:
Alternatives Return No. of
Years
Risk
Govt. Securities 6 15 1
Company deposits 13 3 3
Time deposits 10 5 2
Equity Shares 20 6 5
Construction
business
25 10 1
07
Q.2 (a) What are the characteristics of Linear Programming Problems?
Discuss.
03
(b) Solve problem using graphical method:
Max Z = 20 x1 + 30 x2
Subject to 2x1 + 3x2 ? 120
x1 + x2 ? 40
2x1 + 1.5x2 ? 90
x1, x2 ? 0
04
(c) Solve the following problem using simplex method:
Minimize Z = x1 ? 3x2 + 2x3
Subject to 3x1 ? x2 + 2x3 ? 7
-2x1 + 4x2 + 2x3 ? 12
-4x1 + 3x2 + 8x3 ? 10
x1, x2, x3 ? 0
07
OR
2
(c) Develop dual problem and solve the same:
Max Z = 40 x1 + 50 x2
Subject to 2x1 + 3x2 ? 3
8x1 + 4x2 ? 5
x1, x2 ? 0
Also, find out the result of primal from final table of dual.
07
Q.3 (a) How profit maximization problem can be solved by assignment
Problem?
03
(b) A bank has only one cashier. Cashier working style follows Poisson
distribution with mean service rate of 8 customer per hour. The
customer arrives at a rate of 5 per hour during entire 8 hours. Find
out:
i. Equipment utilization
ii. The percentage time that an arriving customer has to wait.
iii. Average system time.
04
(c) Solve the minimal assignment problem whose matrix as follows:
Also find the other optimal solution, if any.
1 2 3 4
I 2 3 4 5
II 4 5 6 7
III 7 8 9 8
IV 3 5 8 4
07
OR
Q.3 (a) How to tackle the non-square matrix in the assignment problem?
Explain with suitable example.
03
(b) Explain: Kendell?s Notation in terms of Queuing Theory 04
(c) Find out the optimum transportation cost based on given table:
1 2 3 4
Supply
A 4 6 8 13 50
B 13 11 10 8 70
C 14 4 10 13 30
D 9 11 13 8 50
Demand ? 25 35 105 20
07
Q.4 (a) Explain: Procedure for Group Replacement Theory 03
(b) Derive the equation for Economic Order Quantity (EOQ) for constant
demand with the condition of no shortage.
04
(c) The initial price of an equilibrium is Rs. 5000. The running cost varies
as below:
Year 1 2 3 4 5 6 7
Running
Cost
400 500 700 1000 1300 1700 2100
Taking a discount rate of 0.90, find out the optimum replacement
interval.
07
OR
Q.4 (a) Discuss different types of costs associated with inventory. 03
(b) Explain: ABC analysis and its importance. 04
3
(c) Reduce the following game by dominance and find the value of the
game.
Player B
I II III IV
Player A
I 3 2 4 0
II 3 4 2 4
III 4 2 4 0
IV 0 4 0 8
07
Q.5 (a) Explain the concept of ?Expected Value of Perfect Information? in
context of Decision theory.
03
(b) Differentiate: PERT and CPM. 04
(c) XYZ company is currently working with a process which fetches
profit of Rs. 12000. The following alternatives are available to the
company:
i. Do research R1 having success probability of 90% which
costs Rs. 10,000 and if it proves successful it can add gross
income of Rs. 25000.
ii. Do research R2 having success probability of 60% which
costs Rs. 8,000 and if it proves successful it can add gross
income of Rs. 25000.
iii. Pay royalty of Rs. 6000 to third party which can bring gross
income of Rs. 20000.
iv. The company continues the current process.
Because of limited resources, it is assumed that company can for only
one type of research at a time. Use decision tree analysis to find out
optimal strategy.
07
OR
Q.5 (a) Discuss the conditions under which crashing of project is necessary.
Also discuss its effect on the project cost.
03
(b) Explain steps for decision theory approach. 04
(c) A small project is composed of following activities whose time
estimates are listed below:
Activity
Estimated time Duration (in Weeks)
Optimistic Most Likely Pessimistic
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
(a) Draw the project network.
(b) Find the expected duration and variance of each activity.
(c) Calculate early and late occurrence of each event.
07
*************
FirstRanker.com - FirstRanker's Choice
This post was last modified on 20 February 2020