Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R132018 June-July 812AK Operations Research Previous Question Paper
R13
Code No: 812AK
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, June/July- 2018
OPERATIONS RESEARCH
Time: 3 Hours
Max. Marks: 60
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries 8
marks and may have a, b, c as sub questions.
PART - A
5 ? 4 Marks = 20
1.a)
Explain the structure of linear programming problems (LPPs) with an example. [4]
b)
Give the applications of transportation problem in industries.
[4]
c)
Distinguish between gradual failures and sudden failures and their effects.
[4]
d)
Explain the relevance of game theory to managerial problems.
[4]
e)
What is selective inventory control? Why do you optimize this in large industries?[4]
PART - B
5 ? 8 Marks = 40
2.
Use the two-phase simplex method to
Minimize Z = 5x1 + 6x2
Subject to
x1 + x2 5
3x1 + x2 = 10
x1 + 3x2 6
and x1, x2 0
[8]
OR
3.
An animal feed company must produce 200 kg of a mixture consisting of ingredients
X1 and X2 daily. X1 costs Rs. 3 per kg and X2 costs Rs. 8 per kg. Not more than 80 kg of
X1 can be used and at least 60 kg of X2 must be used. Find how much of the each
ingredient should be used if the company wants to minimize the cost? Formulate the above
problem and solve it by simplex method.
[8]
4.a)
What is the difference between transportation problem and an assignment problem?
b)
When does degeneracy occur in transportation problem?
[4+4]
OR
5.
There are five jobs to be assigned on each to 5 machines and associated cost matrix as
follows.
Jobs I
II III IV V
A
11 17 8 16 20
B
9 7
12
6 15
C
13
16
15 12 16
D
21
24 17 28 26
E
14
10 2
11 15
Find the optimum assignment and the associated cost using the assignment technique.[8]
6.
There are six jobs, each of which must go through machines A,B and C. Processing time
(in hours) are given in the following table. Find the sequence that minimizes the total
elapsed time required to complete the following tasks
[8]
Job
1
2
3
4
5
6
Machine A 12
10
9
14
7
9
Machine B 7
6
6
5
4
4
Machine C 6
5
6
4
2
4
OR
7.
1000 bulbs are in use and it costs Rs 10 to replace an individual bulb which has burnt out.
If all bulbs were replaced simultaneously it would cost Rs 4 per bulb. It is proposed to
replace all bulbs at fixed intervals of time, whether or not they have burnt out and to
continue replacing burnt out bulbs as and when they fail.The failure rates have been
observed for certain type of light bulbs are as follows:
Week
1
2
3
4
5
Percent failing by the 10
25
50
80
100
end of week
At what intervals all the bulbs should be replaced? At what group replacements price per
bulb would a policy of strictly individual replacement become preferable to the adopted
policy?
[8]
8.
Find the longest path between the towns A and E using the dynamic programming
approach.
[8]
OR
9.
A company management and the labor union are negotiating a new three year settlement.
Each of these has four strategies.
I: Hard and aggressive bargaining.
II: Reasoning and logical.
III: Legalistic strategy.
IV: Conciliatory approach.
The costs to the company are given for every pair of strategy choice.
What strategy will the two sides adopt? Also determine the value of the game. Use
minimax - maximin rule and then verify your result with dominance rule.
[8]
10.
Monthly demand for an item is 200 units. Ordering cost is Rs. 350, inventory carrying
charge is 24% of the purchase price per year. The purchase prices are P1 =Rs. 10 for
purchasing Q1< 500; P1 = Rs. 9.25 for purchasing 500 Q2< 750 and P3 = Rs. 8.75 for
purchasing 750 < Q3. Determine optimum purchase quantity. If the order cost is reduced to
Rs. 100 per order, compute the optimum purchase quantity.
[8]
OR
11.
Customers arrive at a box office window being managed by a single individual according
to a Poisson input process with mean rate of 30 per hour the time required to serve a
customer has an exponential distribution with a mean of 90 seconds. Find the average
waiting time of a customer. Also determine the average number of customers in the system
and average queue length.
[8]
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This post was last modified on 17 March 2023