Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 7th Sem New 2171901 Operation Research Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2171901 Date:16/05/2019
Subject Name:Operation Research
Time:02:30 PM TO 05:00 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) Write applications of operation research.
03
(b) Differentiate CPM & PERT.
04
(c) Using graphical method to solve the LPP
Max Z=3x1+4x2
Subjected to,
1) 5x1+4x2 ?200,
2) 3x1+5x2 ?150,
3) 5x1+4x2 ?100
4) 8x 1+4x 2 ?80 x 1 & x 2 ?0
07
Q.2 (a) Construct the dual of following prime problem
Maximize Z = 3 x 1 - x 2 + x 3
Subject to constraints,
4x 1 ? x 2 ? 8, 8x 1 + x 2 + 3x 3 ? 8,
5x 1 -6 x 3 ? 12,
x 1, x 2, x 3 ? 0
03
(b) A company is manufacturing two different types of products, A and B. Each
product has to be processed on two machines M1 and M2.Product A requires 2
hours on machine M1 and 1 hour on machine M2, Product B requires 1 hours
on machine M1 and 2 hour on machine M2.The available capacity of machine
M1 is 104 hours and that of machine M2 is 76 hours. Profit per unit for product
A is Rs.6 and that for B is Rs.11.Formulate the problem.
04
(c) Solve the following LPP by simplex method.
Maximize Z= 40x1 +35x2
Subjected to 2x1+3x2 ? 60
4x1+3x2 ? 96
x1,x2 ? 0
07
OR
(c) Solve the following LPP by simplex method
Maximize Z=3x1+2x2
Subjected to 2x1+x2 ? 40
2x1+3x2 ? 60
x1+x2 ? 24
x1,x2 ? 0
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2171901 Date:16/05/2019
Subject Name:Operation Research
Time:02:30 PM TO 05:00 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) Write applications of operation research.
03
(b) Differentiate CPM & PERT.
04
(c) Using graphical method to solve the LPP
Max Z=3x1+4x2
Subjected to,
1) 5x1+4x2 ?200,
2) 3x1+5x2 ?150,
3) 5x1+4x2 ?100
4) 8x 1+4x 2 ?80 x 1 & x 2 ?0
07
Q.2 (a) Construct the dual of following prime problem
Maximize Z = 3 x 1 - x 2 + x 3
Subject to constraints,
4x 1 ? x 2 ? 8, 8x 1 + x 2 + 3x 3 ? 8,
5x 1 -6 x 3 ? 12,
x 1, x 2, x 3 ? 0
03
(b) A company is manufacturing two different types of products, A and B. Each
product has to be processed on two machines M1 and M2.Product A requires 2
hours on machine M1 and 1 hour on machine M2, Product B requires 1 hours
on machine M1 and 2 hour on machine M2.The available capacity of machine
M1 is 104 hours and that of machine M2 is 76 hours. Profit per unit for product
A is Rs.6 and that for B is Rs.11.Formulate the problem.
04
(c) Solve the following LPP by simplex method.
Maximize Z= 40x1 +35x2
Subjected to 2x1+3x2 ? 60
4x1+3x2 ? 96
x1,x2 ? 0
07
OR
(c) Solve the following LPP by simplex method
Maximize Z=3x1+2x2
Subjected to 2x1+x2 ? 40
2x1+3x2 ? 60
x1+x2 ? 24
x1,x2 ? 0
07
2
Q.3 (a) Draw the network diagram for given relationship of activities
Activity A B C D E F G H
Predecessor - - A B B C D E,F,G
07
(b) The maintenance cost and resale value per year of a machine whose purchase
price is Rs.7000 is given below.When should machine be replaced.
Year
1 2 3 4 5 6 7 8
Maintenance
cost (Rs)
900 1200 1600 2100 2800 3700 4700 5900
Resale value
cost (Rs)
4000 2000 1200 600 500 400 400 400
07
OR
Q.3 (a) Solve the following pay-off matrix for player A. Also find out the optimal
strategies and value of the game.
Player B
B1 B2 B3
Player
A
A1 275 -50 -75
A2 125 130 150
07
(b) Determine the critical path and project duration for given activities.
Activity
A B C D E F G
Predecessor activity - A A A B,C C,D E,F
Duration(Days) 10 5 4 7 6 4 7
07
Q.4 (a) What is assignment problem? Show the assignment problem is special case of
transportation problem.
03
(b) Describe the various steps in Hungarian method used for solving the
assignment problem.
04
(c) For Asia cup Rohit Sharma as a captain of india has to allot five middle batting
positions to five batsmen. The average runs scored by each batsman at these
positions are as follows.
Batting Position ?
Batsman?
I II III IV V
Rayudu 40 40 35 25 50
Dhoni 42 30 16 25 27
Rohit 50 48 40 60 50
Karthik 20 19 20 18 25
Dhawan 58 60 59 55 53
Find the assignments to batsmen position which would give maximum number
of runs and which will help to get the Asia cup.
07
(OR)
Q.4 (a) What is degeneracy in transportation problem?
03
Q.4 (b) The paper manufacturing company has three warehouses located in three
different areas A, B, C. The company has to send from these warehouse to three
destinations, says D,E, and F. The availability from warehouse A,B and C and
demand at D,E and F is given in following table. Find out basic feasible
solution.(Use any method)
04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2171901 Date:16/05/2019
Subject Name:Operation Research
Time:02:30 PM TO 05:00 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) Write applications of operation research.
03
(b) Differentiate CPM & PERT.
04
(c) Using graphical method to solve the LPP
Max Z=3x1+4x2
Subjected to,
1) 5x1+4x2 ?200,
2) 3x1+5x2 ?150,
3) 5x1+4x2 ?100
4) 8x 1+4x 2 ?80 x 1 & x 2 ?0
07
Q.2 (a) Construct the dual of following prime problem
Maximize Z = 3 x 1 - x 2 + x 3
Subject to constraints,
4x 1 ? x 2 ? 8, 8x 1 + x 2 + 3x 3 ? 8,
5x 1 -6 x 3 ? 12,
x 1, x 2, x 3 ? 0
03
(b) A company is manufacturing two different types of products, A and B. Each
product has to be processed on two machines M1 and M2.Product A requires 2
hours on machine M1 and 1 hour on machine M2, Product B requires 1 hours
on machine M1 and 2 hour on machine M2.The available capacity of machine
M1 is 104 hours and that of machine M2 is 76 hours. Profit per unit for product
A is Rs.6 and that for B is Rs.11.Formulate the problem.
04
(c) Solve the following LPP by simplex method.
Maximize Z= 40x1 +35x2
Subjected to 2x1+3x2 ? 60
4x1+3x2 ? 96
x1,x2 ? 0
07
OR
(c) Solve the following LPP by simplex method
Maximize Z=3x1+2x2
Subjected to 2x1+x2 ? 40
2x1+3x2 ? 60
x1+x2 ? 24
x1,x2 ? 0
07
2
Q.3 (a) Draw the network diagram for given relationship of activities
Activity A B C D E F G H
Predecessor - - A B B C D E,F,G
07
(b) The maintenance cost and resale value per year of a machine whose purchase
price is Rs.7000 is given below.When should machine be replaced.
Year
1 2 3 4 5 6 7 8
Maintenance
cost (Rs)
900 1200 1600 2100 2800 3700 4700 5900
Resale value
cost (Rs)
4000 2000 1200 600 500 400 400 400
07
OR
Q.3 (a) Solve the following pay-off matrix for player A. Also find out the optimal
strategies and value of the game.
Player B
B1 B2 B3
Player
A
A1 275 -50 -75
A2 125 130 150
07
(b) Determine the critical path and project duration for given activities.
Activity
A B C D E F G
Predecessor activity - A A A B,C C,D E,F
Duration(Days) 10 5 4 7 6 4 7
07
Q.4 (a) What is assignment problem? Show the assignment problem is special case of
transportation problem.
03
(b) Describe the various steps in Hungarian method used for solving the
assignment problem.
04
(c) For Asia cup Rohit Sharma as a captain of india has to allot five middle batting
positions to five batsmen. The average runs scored by each batsman at these
positions are as follows.
Batting Position ?
Batsman?
I II III IV V
Rayudu 40 40 35 25 50
Dhoni 42 30 16 25 27
Rohit 50 48 40 60 50
Karthik 20 19 20 18 25
Dhawan 58 60 59 55 53
Find the assignments to batsmen position which would give maximum number
of runs and which will help to get the Asia cup.
07
(OR)
Q.4 (a) What is degeneracy in transportation problem?
03
Q.4 (b) The paper manufacturing company has three warehouses located in three
different areas A, B, C. The company has to send from these warehouse to three
destinations, says D,E, and F. The availability from warehouse A,B and C and
demand at D,E and F is given in following table. Find out basic feasible
solution.(Use any method)
04
3
Destinations
D E F Supply
Source
A 4 5 1 40
B 3 4 3 60
C 6 2 8 70
Demand 70 40 60
Q.4 (c) Find the optimal solution of the following Transportation problem using MODI
method. Use VAM to find IBFS.
Destinations
M1 M2 M3 M4 Supply
Source
A 3 2 4 1 20
B 2 4 5 3 15
C 3 5 2 6 25
D 4 3 1 4 40
Demand 30 20 25 25
07
Q.5 (a) What is inventory? Classify the inventory.
03
(b) Explain the different methods useful for decision making under certainty.
04
(c) The annual demand for an item is 3200 units. The unit cost is Rs.6 and
inventory carrying charges 25 % per annum.If the cost of one procurement is
Rs.150,then determine the 1) EOQ 2) No. of order per year 3) Time between
two consecutive order 4) The optimal cost.
07
OR
Q.5 (a) Define the following terms relating the customer?s behavior in Queue.
a) Balking b) Jockeying c) Reneging
03
(b) Write a short note on ?ABC analysis? of inventory control technique.
04
(c) Customers arrive at one person barber shop according to Poisson process with
a mean inter-arrival time 20 minutes. Customer spends on an average of 15
minutes in barber?s chair.
1) What is the probability that new arrival need not wait for the barber to
be free?
2) What is the expected number of customers in barber shop?
3) How much time can a customer expect to wait for his turn?
4) How much time can a customer spend in the shop?
5) Management will put in another chair and hire another barber when
customer?s average time in shop exceeds 1.25 hours. How much must
average rate of arrival increase to warrant a second barber.
07
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This post was last modified on 20 February 2020