Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 5th Sem 3151910 Operation Research Previous Question Paper
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?V (NEW) EXAMINATION ? WINTER 2020
Subject Code:3151910 Date:05/02/2021
Subject Name:Operation Research
Time:10:30 AM TO 12:30 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 (a) State various phases of Operations Research problem.
03
(b) Briefly explain the characteristics of Operations Research.
04
(c) A paper mill produces paper for books as well as for magazines. Each kg of paper for 07
books requires 2 kg of material A and 3 kg of material B. for magazines, the proportion
is 2 kg of A and 2 kg of B for each kg of paper. The mill need 15000 kg paper for books
and 6000 kg for magazines. Materials A and B are available as 3 and 5 lakhs kg
respectively. Requirements of books is twice that for magazines. Selling price per book
paper is Rs. 14 per kg and for magazines it is Rs. 10 per kg. cost of material A is Rs. 2
per kg and that for material B is Rs. 2.5 per kg. Formulate LP model for paper mill to
maximize the total profit.
Q.2 (a) Write at least five application areas of Linear Programming.
03
(b) Discuss basic assumptions in Linear Programming.
04
(c) Solve the following LP problems using Simplex Method.
07
Maximise Z = 10x + 15 y + 20 z
S.T.
10 x+ 5y + 2z 2,700
5x + 10y + 4z 2,200
x + y + 2z 500 and
All x, y and z are 0
Q.3 (a) Explain the following terms:
03
a. Shadow price
b. Opportunity cost
(b) Briefly explain unbalanced assignment problem.
04
(c) A company manufacturing air coolers has two plants located at Mumbai and Kolkata 07
with a capacity of 200 units and 100 units per week respectively. The company supplies
the air cooler to its four show rooms located at Ranchi, Delhi, Lucknow and Kanpur
which have a maximum demand of 75, 100, 100, and 30 units respectively. Due to the
differences in raw material cost and transportation cost, the profit per unit in rupees
differs which is given below.
Ranchi
Delhi
Lucknow
Kanpur
Mumbai
90
90
100
110
Kolkata
50
70
130
85
Solve the transportation problem to maximize the profit.
Q.4 (a) Give mathematical model for transportation problem.
03
(b) Define the term Decision theory. Describe decision models based on the criterion of 04
degree of certainty.
1
(c) Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at five stations 07
I, II, III, IV and V. The mileage between various stations are given by the table below.
How should the wagons be transported so as to minimize total mileage covered?
I
II
III
IV
V
1
10
5
9
18
11
2
13
9
6
12
14
3
3
2
4
4
5
4
18
9
12
17
15
5
11
6
14
19
10
Q.5 (a) Explain the queuing model as indicated by the following notations.
03
M/D/1 : FCFS//
(b) The following matrix gives the payoff of different strategies (alternatives) A, B, and C 04
against conditions (events) W, X, Y and Z. Identify the decision taken under the
following approaches:
a. Regret,
b. Hurwicz criterion. The decision maker's degree of optimism () being 0.7.
Events
W
X
Y
Z
Rs.
Rs.
Rs.
Rs.
A
4000
?100
6000
18000
B
20000
5000
400
0
C
20000 15000 ? 2000 1000
(c) A mechanic is to be recruited to repair scooters that breakdown at an average rate of 6 07
per hour. The breakdowns follow a Poisson distribution. Non-productive time of a
scooter costs Rs. 40 per hour. Mechanics A and B have been interviewed for the purpose.
Mechanic A charges Rs. 20 per hour, and services scooters at the rate of 8 per hour.
Mechanic B charges Rs. 28 per hour, and services 12 scooters per hour, on an average.
Which one of the two should be recruited and why? Assume an 8 hours of work each
day.
Q.6 (a) What is replacement? Explain by means real world examples.
03
(b) Differentiate between PERT and CPM.
04
(c) The maintenance cost and resale value per year of a machine whose 07
purchase price is Rs. 7000/- is given below:
Year
1
2
3
4
5
6
7
8
Maintenance cost in Rs. 900
1200 1600 2100 2800 3700 4700 5900
Resale value in Rs.
4000 2000 1200 600
500
400
400
400
When should the machine be replaced?
Q.7 (a) Define following:
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a. Saddle Point
b. Pure Strategy
c. Mixed Strategy
(b) Discuss the rules of network construction
04
(c) A and B play a game in which each has three coins: 5 paise, 10 paise, and 20 paise coin. 07
Each player selects a coin without the knowledge of the other's choice. If the sum of the
coins is an odd amount, A wins B's coin, and if the sum is even, B wins A's coin. Find
the best strategy for each player and the value of the game.
Q.8 (a) Briefly explain Decision Tree
03
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(b) Discuss all four types of Floats.
04
(c) There are seven activities in a project and the time estimates are as follows:
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Immediate
Optimistic
Most Likely
Pessimistic
Activity Predecessor
Time
Time
Time
A
?
2
6
10
B
?
4
6
12
C
A
2
3
4
D
A
2
4
6
E
B, D
3
6
9
F
B, C, D
6
10
14
G
F
1
3
5
Draw activity on node network for the project. Calculate expected project duration and
variance for each activity.
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This post was last modified on 04 March 2021