Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 6th Sem New 2163201 Operation Research Previous Question Paper
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (New) EXAMINATION ? WINTER 2019
Subject Code: 2163201 Date: 04/12/2019
Subject Name: Operation Research
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
? Attempt all questions.
? Make suitable assumptions wherever necessary.
? Figures to the right indicate full marks.
MARKS
Q.1* (a) Discuss areas of application of operation research. 03
(b) A firm is engaged in producing two products, A and B. Each unit of
product A requires 2 kg of raw material and 4 labor hours for processing,
whereas each unit of product B requires 3 kg of raw material and 3 hours
of labor, of the same type. Every week, the firm has an availability of 60
kg of raw material and 96 labor hours. One unit of product A sold yields
Rs 40 and one unit of product B sold gives Rs 35 as profit.
Formulate this problem as linear programming problem to determine as to
know how many units of each of the products should be produced per week
so that the firm can earn the maximum profit. Assume that there is no
marketing constraint so that all that is produced can be sold.
04
(c) Explain methodology of operation research. 07
Q.2 (a) Illustrate graphically
1) No feasible solution 2) Unbounded solution
03
(b) Solve graphically the following LPP:
Maximize z=8x1 + 16x2
Subject to,
x1 + x2 ? 200 , x2 ? 125, 3x1 +6x2 ? 900 , x1, x2 ? 0
04
(c) Explain simplex method for solving linear programming problem. 07
OR
(c) Solve the following LPP using simplex method.
Maximize z=3x1 + 5x2
Subject to,
x1 + 2x2 ? 2000, x1 + x2 ? 1500, x2 ? 600, x1, x2 ? 0
07
Q.3 (a) Discuss North-West and Least cost method for finding initial basic
solution.
03
(b) Discuss assignment algorithm. 04
(c) Using Big-M method solve the following problem
Minimize z=60x1 + 80x2
Subject to,
20x1 + 30x2 ? 900, 40x1 + 30x2 ? 1200, x1, x2 ? 0
07
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (New) EXAMINATION ? WINTER 2019
Subject Code: 2163201 Date: 04/12/2019
Subject Name: Operation Research
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
? Attempt all questions.
? Make suitable assumptions wherever necessary.
? Figures to the right indicate full marks.
MARKS
Q.1* (a) Discuss areas of application of operation research. 03
(b) A firm is engaged in producing two products, A and B. Each unit of
product A requires 2 kg of raw material and 4 labor hours for processing,
whereas each unit of product B requires 3 kg of raw material and 3 hours
of labor, of the same type. Every week, the firm has an availability of 60
kg of raw material and 96 labor hours. One unit of product A sold yields
Rs 40 and one unit of product B sold gives Rs 35 as profit.
Formulate this problem as linear programming problem to determine as to
know how many units of each of the products should be produced per week
so that the firm can earn the maximum profit. Assume that there is no
marketing constraint so that all that is produced can be sold.
04
(c) Explain methodology of operation research. 07
Q.2 (a) Illustrate graphically
1) No feasible solution 2) Unbounded solution
03
(b) Solve graphically the following LPP:
Maximize z=8x1 + 16x2
Subject to,
x1 + x2 ? 200 , x2 ? 125, 3x1 +6x2 ? 900 , x1, x2 ? 0
04
(c) Explain simplex method for solving linear programming problem. 07
OR
(c) Solve the following LPP using simplex method.
Maximize z=3x1 + 5x2
Subject to,
x1 + 2x2 ? 2000, x1 + x2 ? 1500, x2 ? 600, x1, x2 ? 0
07
Q.3 (a) Discuss North-West and Least cost method for finding initial basic
solution.
03
(b) Discuss assignment algorithm. 04
(c) Using Big-M method solve the following problem
Minimize z=60x1 + 80x2
Subject to,
20x1 + 30x2 ? 900, 40x1 + 30x2 ? 1200, x1, x2 ? 0
07
OR
Q.3 (a) Discuss Vogel?s approximation method for finding initial basic solution. 03
(b) Write the dual of the following LPP
Minimize z=10x1 + 20x2
Subject to,
3x1 + 2x2 ? 18, x1 + 3x2 ? 8, 2x1 - x2 ? 6, x1, x2 ? 0
04
(c) Using the two-phase method solve the following problem
Minimize z=150x1 + 150x2 + 100x3
Subject to,
2x1 + 3x2 + x3 ? 4, 3x1 + 2x2 + x3 ? 3, x1, x2, x3 ? 0
07
Q.4 (a) Define interfering float, free float and independent float.
03
(b) Discuss various methods to generate random numbers.
04
(c) A tailor specializes in ladies? dresses. The number of customers
approaching the tailor appears to be Poison distributed with a mean of 6
customers per hour. The tailor attends the customers on a first come first
served basis and the customers wait if the need be. The tailor can attend
the customers at an average rate of 10 customers per hour with the service
time exponentially distributed.
Find
1) The utilization parameter
2) The probability that the system is idle
3) The average time that the tailor is free on a 10-hour working day
4) The probability of exactly one customer in queuing system
5) Expected number of customers in tailor?s shop
6) Expected number of customers waiting for tailor?s service
7) Expected time customer will spend in tailor?s shop
07
OR
Q.4 (a) A firm is using a machine whose purchase price is Rs 13000. The
installation charges amount to Rs 3600 and the machine has a scrap value
of Rs 1600. The maintenance cost in various years is given in the following
table.
Year 1 2 3 4 5 6 7 8 9
Cost(Rs) 250 750 1000 1500 2100 2900 4000 4800 6000
Determine after how many years the machine should be replaced assuming
that machine replacement can be done only at the year ends.
03
(b) What is simulation? What are the advantages and disadvantages of
simulation?
04
(c) Information on the activities required for a project is as follows
Name A B C D E F G H I J K
Activities 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
Draw the network and calculate the earliest start (ES), earliest finish (EF),
latest start (LS) and latest finish (LF) time for each of the activities. Also
find critical path and time required to complete the project.
07
FirstRanker.com - FirstRanker's Choice
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? VI (New) EXAMINATION ? WINTER 2019
Subject Code: 2163201 Date: 04/12/2019
Subject Name: Operation Research
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
? Attempt all questions.
? Make suitable assumptions wherever necessary.
? Figures to the right indicate full marks.
MARKS
Q.1* (a) Discuss areas of application of operation research. 03
(b) A firm is engaged in producing two products, A and B. Each unit of
product A requires 2 kg of raw material and 4 labor hours for processing,
whereas each unit of product B requires 3 kg of raw material and 3 hours
of labor, of the same type. Every week, the firm has an availability of 60
kg of raw material and 96 labor hours. One unit of product A sold yields
Rs 40 and one unit of product B sold gives Rs 35 as profit.
Formulate this problem as linear programming problem to determine as to
know how many units of each of the products should be produced per week
so that the firm can earn the maximum profit. Assume that there is no
marketing constraint so that all that is produced can be sold.
04
(c) Explain methodology of operation research. 07
Q.2 (a) Illustrate graphically
1) No feasible solution 2) Unbounded solution
03
(b) Solve graphically the following LPP:
Maximize z=8x1 + 16x2
Subject to,
x1 + x2 ? 200 , x2 ? 125, 3x1 +6x2 ? 900 , x1, x2 ? 0
04
(c) Explain simplex method for solving linear programming problem. 07
OR
(c) Solve the following LPP using simplex method.
Maximize z=3x1 + 5x2
Subject to,
x1 + 2x2 ? 2000, x1 + x2 ? 1500, x2 ? 600, x1, x2 ? 0
07
Q.3 (a) Discuss North-West and Least cost method for finding initial basic
solution.
03
(b) Discuss assignment algorithm. 04
(c) Using Big-M method solve the following problem
Minimize z=60x1 + 80x2
Subject to,
20x1 + 30x2 ? 900, 40x1 + 30x2 ? 1200, x1, x2 ? 0
07
OR
Q.3 (a) Discuss Vogel?s approximation method for finding initial basic solution. 03
(b) Write the dual of the following LPP
Minimize z=10x1 + 20x2
Subject to,
3x1 + 2x2 ? 18, x1 + 3x2 ? 8, 2x1 - x2 ? 6, x1, x2 ? 0
04
(c) Using the two-phase method solve the following problem
Minimize z=150x1 + 150x2 + 100x3
Subject to,
2x1 + 3x2 + x3 ? 4, 3x1 + 2x2 + x3 ? 3, x1, x2, x3 ? 0
07
Q.4 (a) Define interfering float, free float and independent float.
03
(b) Discuss various methods to generate random numbers.
04
(c) A tailor specializes in ladies? dresses. The number of customers
approaching the tailor appears to be Poison distributed with a mean of 6
customers per hour. The tailor attends the customers on a first come first
served basis and the customers wait if the need be. The tailor can attend
the customers at an average rate of 10 customers per hour with the service
time exponentially distributed.
Find
1) The utilization parameter
2) The probability that the system is idle
3) The average time that the tailor is free on a 10-hour working day
4) The probability of exactly one customer in queuing system
5) Expected number of customers in tailor?s shop
6) Expected number of customers waiting for tailor?s service
7) Expected time customer will spend in tailor?s shop
07
OR
Q.4 (a) A firm is using a machine whose purchase price is Rs 13000. The
installation charges amount to Rs 3600 and the machine has a scrap value
of Rs 1600. The maintenance cost in various years is given in the following
table.
Year 1 2 3 4 5 6 7 8 9
Cost(Rs) 250 750 1000 1500 2100 2900 4000 4800 6000
Determine after how many years the machine should be replaced assuming
that machine replacement can be done only at the year ends.
03
(b) What is simulation? What are the advantages and disadvantages of
simulation?
04
(c) Information on the activities required for a project is as follows
Name A B C D E F G H I J K
Activities 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
Draw the network and calculate the earliest start (ES), earliest finish (EF),
latest start (LS) and latest finish (LF) time for each of the activities. Also
find critical path and time required to complete the project.
07
Q.5 (a) A firm owns facilities at 7 places. It has manufacturing plants at places A,
B, C with daily output of 500, 300 and 200. It has warehouses at places P,
Q, R, S with daily requirement of 180, 150, 350, 320 units respectively.
Per unit shipping charge is given below
To: P Q R S
From A 12 10 12 13
From B 7 11 8 14
From C 6 16 11 7
Find the transportation cost by Vogel?s approximation method.
03
(b) A production supervisor is considering how he should assign the four jobs
that are to be performed, to four of the workers. He wants to assign the jobs
to workers such that the aggregate time to perform the jobs is the least. The
information for the time taken is given below
Worker Job
A B C D
1 45 40 51 67
2 57 42 63 55
3 49 52 48 64
4 41 45 60 55
Solve this assignment problem using Hungarian Assignment Method.
04
(c) A bakery keeps stock of popular brand of cake. Previous experience shows
that the daily demand pattern is given below
Daily
Demand
0 10 20 30 40 50
Probability 0.01 0.2 0.15 0.5 0.12 0.02
Use the following sequence of random numbers to simulate demand foe
next 10 days and also find average demand per day.
Random Numbers:- 25, 39 ,65, 76, 12, 05, 73, 89, 19, 49
07
OR
Q.5 (a) Explain various elements of queuing system. 03
(b) Explain group replacement policy with suitable example. 04
(c) Discuss PERT, CPM and difference between PERT and CPM. 07
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This post was last modified on 20 February 2020