Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R15 2020 November 821AJ October November Operations Research Previous Question Paper
S OCT 2020
Code No: 821AJ
R15
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, October / November - 2020
OPERATIONS RESEARCH
Time: 2 Hours
Max.Marks:75
Answer any five questions
All questions carry equal marks
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1.
A company manufactures two kinds of machines, each requiring a different
manufacturing technique. The deluxe machine requires 18 hours of labour, 8 hours of
testing and yields a profit of Rs.400. The standard machine requires 3 hours of labour,
4 hours of testing and yields a profit of Rs.200. There are 800 hours of labour and
600 hours of testing available each month. A marketing forecast has shown that the
monthly demand for the standard machine is to be more than 150. The management
wants to know the number of each model to be produced monthly that will maximize
total profit. Formulate and solve this as a linear programming problem.
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used
2.
A nutrition scheme for babies is proposed by a committee of doctors. Babies can be
given two types of food (I and II) which are available in standard sized packets
weighing 50 grams. The cost per packet of these foods are Rs.2 and Rs.3. The Vitamin
availability in each type of food per packet and the minimum vitamin requirement for
each type of vitamin are summarized in table below:
Vitamin
Vitamin availability Vitamin availability Minimum
daily
in type I food
in type I I food
required vitamin
1
1
1
6
2
7
1
14
Cost/packet Rs.
2
3
Develop a linear programming model to determine the optimal combination of
food types with the minimum cost such that the minimum requirement of vitamin in
each type is satisfied solve it by simplex method.
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3.
A company as three factories at Amethi, Baghpat and Gwalior having production
capacity of 5,000, 6,000 and 2,500 tonnes respectively. Four distribution centres at
Allahabad, Bombay , Kolkata and Delhi requiring 6,000 tonnes 4,000 tonnes, 2,000
tonnes and 1,500 tonnes respectively of the product. The transportation costs in
thousands of rupees per tonne from different factories to different centres are given as
below:
Distribution centres
factories
Allahabad
Bombay
Kolkata
Delhi
Amethi
3
2
7
6
Bagphat
7
5
2
3
Gwalior
2
3
4
5
Suggest an optimum schedule and find the minimum cost of transportation.
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S OCT 2020
4.
Consider the problem of assigning four sales persons to four different sales regions as
shown below such that the total sales are maximized.
Sales region
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1 2 3 4
Sales man A
5
11
8
9
B
5
7
9
7
C
7
8
9
9
D
6
8
11
12
The cell entries represent annual sales figures in crore of rupees. Find the optimal
allocation of the sales persons to different regions.
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5.
Find the sequence that minimizes the total time required in performing the following
jobs on three machines in the order ABC. Processing time in hours are given in the
following table:
Job
1
2
3
4
5
M/c A
8
10
6
7
11
M/c B
5
6
2
3
4
used
M/c C
4
9
8
6
5
What is the total processing time for all the 5 jobs? Also find the idle time on each
machine.
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6.
A company is planning to replace an equipment by a new equipment whose first cost is
Rs.1,00,000. The operating and maintenance cost of the equipment during its first year
of operation is Rs.10,000 and it increases by Rs.2,000 every year thereafter. The resale
value of the equipment at the end of the first year of its operation is Rs.65,000 and it
decreases by Rs.10,000 every year thereafter. Find the economic life of the equipment
by assuming the interest rate as 12%.
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7.
Consider 4 ? 4 game played by Players A and B and solve it optimally:
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Player B
1 2 3 4
Player A1
6
2
4
8
A2
2
-1
1
12
A3
2
3
3
9
A4
5
2
6
10
8.
In a railway marshalling yard, goods trains arrive at a rate of 30 trains per day.
Assuming that the inter-arrival time follows an exponential distribution and the service
time (the time taken to hump the train) distribution is also exponential with an average
of 36 minutes. Calculate
a) Expected queue size (line length)
b) Probability that the queue size exceeds 10.
c) If the input of trains increases to an average of 33 per day, what will the change in
a and b?
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This post was last modified on 17 March 2023