Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R132019 April-May 812AK Operations Research Previous Question Paper
R13
Code No: 812AK
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, April/May - 2019
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) What are the shadow prices? What is its significance in simplex method of solving LPP?
[4]
b)
What is the difference between transportation problem and an assignment problem?
[4]
c)
What are the conditions recommended for the replacement of a machine with a new one when
you already have an old one?
[4]
d)
Distinguish between the games with saddle points and games without saddle points.
[4]
e)
What are the assumptions used in deriving EOQ formula?
[4]
PART - B
5? 8 Marks = 40
2.
Solve the following LPP using graphical method.
Maximize
Z = 10x1 + 8x2
Subject to
xl + 2x2 1000
x1 300
x2 500;
and x1, x2 0
[8]
OR
3.
A company wants to purchase at most 180 units of a product. There are two types of
the product, M1 and M2 available. M1 occupies 2 ft3, cost Rs. 12/- and the company
makes a profit of Rs. 3/-. M2 occupies 3ft3, costs Rs. 15/- and the company makes a
profit of Rs 4/- If the budget is Rs. 15,000/- and the warehouse has 3000 ft3 for
product. Formulate the problem as a linear programming model and solve the
problem using simplex method.
[8]
4.
Solve the following transportation problem, i.e., find the optimal solution, where the
entries are cost coefficients.
[8]
To Destination
Availability
1
2
3
4
1
15
0
20
10
50
From
2
15
8
11
20
50
Origins
3
0
16
14
18
100
Requirement
30
40
60
70
200
OR
5.
Four salesmen are to be assigned to four districts. Estimates of the sales revenue is
hundred of Rs. for each salesmen are as follows: Give the assignment pattern that
maximizes the sales revenue.
[8]
6.
Find the sequence that minimizes the total elapsed time (in hours) required to complete
the following tasks. Each job is processed in the order ABC.
[8]
JOB
1
2
3
4
5
6
7
Machine A
12 6
5
11 5
7
6
Machine B
7
8
9
4
7
8
3
Machine C
3
4
1
5
2
3
4
OR
7.
The mortality rates as obtained for an electronic component are noted in the table below
Month
1
2
3
4
5
6
Percentage fails at the end of the month 8
22
45
70
85
100
There are 1500 items in operation. It costs Rs. 20 to replace an individual item and
Re.0.50 per item if all items are replaced simultaneously. It is decided to replace all items
at fixed intervals and to continue replacing individual item as and when they fail. At what
intervals should all items be replaced?
[8]
8.
The routes of an airline which connects 16 cities (A,B....P) are shown in fig. below.
Journey from one city to another is possible only along the lines (routes). Shown with the
associated costs indicated on the path segments. If a person wants to travel from city A to
City P with minimum costs, without any back tracking, determine the optimal path
(route) using dynamic programming.
[8]
OR
9.
A and B play a game in which each has three coins a 5 paise, a 10 paise and a 20 paise.
Each selects a coin without the knowledge of the others choice. If the sum of the coins is
an odd amount, A wins B's coins. If the sum is even B wins A's coins. Find the best
strategy for each player and the value of the game.
[8]
10.
The demand of an item is uniform at a rate of 20 units per month. The fixed cost is Rs. 10
each time a production run is made. The production cost is Rs 1 per item and the
inventory carrying cost is Rs. 0.25 per item per month. If the shortage cost is Rs. 1.25 per
item per month, determine how often to make a production run and of what size should it
be?
[8]
OR
11.
A T.V. repairman finds that the time spent on his jobs have an exponential distribution
with mean of 30 minutes. If he repairs sets in the order in which they come in, and if the
arrival of sets is approximately Poisson distribution with an average rate of 10 per 8 hour
day, what is repairmen's expected idle time each day? How many jobs are ahead of the
average set just brought in?
[8]
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This post was last modified on 17 March 2023