Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R17 2018 June-July 842AD Operations Research Previous Question Paper
R17
Code No: 842AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, June/July - 2018
OPERATIONS RESEARCH
Time: 3hrs
Max.Marks:75
Note: This question paper contains two parts A and B.
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.
PART - A
5 ? 5 Marks = 25
1.a) State the degeneracy in the transportation problem. How is it resolved?
[5]
b) State the optimal policy for replacement when time value of money is considered.[5]
c) State the assumptions of M/M/c queuing model.
[5]
d) State the optimal policy for single period stochastic demand model.
[5]
e) State the dominance rules for the solving the Game theory problems without saddle point.
[5]
PART - B
5 ? 10 Marks = 50
2.a) Define Model. Explain about various types of models with respect to their
physical configuration.
b) The ABC company wishes to plan its advertising strategy. There are two media under
consideration, call them magazines I and II. Magazine I has a reach of 2000 potential
customers and magazine II has a reach of 3000 potential customers. The cost of page of
advertising is Rs.400 and Rs.600 for magazines I and II respectively. The firm has a
monthly budget of Rs.6000. There is an important requirement that the total reach for the
income group under Rs.20000 per annum, should not exceed 4000 potential customers.
The reach in magazine I and magazine II for this income group is 400 and 200 potential
customers. How many pages should be brought in the two magazines to maximize the
total reach? Formulate the problem as LPP. Solve it by Graphical method.
[5+5]
OR
3.
A company has three factories I,II,III and four warehouses 1, 2, 3, 4.
The transportation cost (in Rs.) per unit from each factory to each ware house is given in
table. The requirements of each warehouse and the capacity of each factory are given
below.
Warehouse
1
2
3
4
Availability
Factory
I
25 17
25
14
400
II
15 10
18
24
600
III
16 20
8
13
600
Requirement
300 300
500
500
Find the minimum cost of transportation schedule. Use least cost method to generate
initial BFS.
[10]
4.a) State the traveling salesman problem.
b) Give the following across city distance table, find the minimum distance root provided his
home town is in A
[5+5]
To
From A
B
C D E
A
7
6
8
4
B
7
8
5
3
C
6
8
9
7
D
8
5
9
8
E
4
6
7
8
Find the assignment of salesmen to various districts which will yield maximum profit?
OR
5.a) State the group replacement policy
b) The following failure rates have been observed for a certain type of light bulbs:
End of week Probability of failure to date
1
0.05
2
0.13
3
0.25
4
0.43
5
0.68
6
0.88
7
0.96
8
1.00
The cost of replacing an individual failed bulb is Rs.1.25. The decision is made to replace
all bulbs simultaneously at fixed intervals and also to replace individual bulbs as they fall
in service. If the cost of group replacement is 30 paise per bulb, what is the best interval
between group.
[5+5]
6.a) Explain how the queues are classified and give their notations
b) In a bank, cheques are cashed at a single "teller" counter. Customers arrive at the counter
in a Poisson manner at an average rate of 30 customers/hr. The teller takes on an average
1.5 minutes to cash cheque. The service time has been shown to be exponentially
distributed.
i) Calculate the percentage of time the teller is busy.
ii) Calculate the average time a customer is expected to wait.
[5+5]
OR
7.
Customers arrive at one ?window drive-in bank according to a Poisson distribution with
mean of 10 per hour. Service time per customer is exponential with a mean of 5 minutes.
The space in front of the window, including that for the serviced car, can accommodate a
maximum of 3 cars. The other cars can wait outside this space.
a) What is the probability that an arriving customer can drive directly to the space in front
of the window?
b) What is the probability that an arriving customer will have to wait outside the indicated
space?
c) How long is an arriving customer expected to wait before starting service?
[10]
8.
If a product is to be manufactured within the company, the details are as follows:
Annual demand rate, r=36000 units
Production rate, k=72000 units
Setup cost, C0=Rs. 250 per setup
Carrying cost, Cc= Rs.25/unit/year.
Find the a) EOQ and b) Cycle time after deriving relevant expressions.
[10]
OR
9.
Annual demand for an item is 5400 units. Ordering cost is Rs.400 per order. Inventory
carrying cost is 30% of the purchase price/unit/year. The price breaks are shown as:
Quantity Price(Rs.)
0Q1< 2400
12
2400Q2<3000
10
3000Q3
08
______________________________________________________________________
Find the optimal order size. If the order cost is changed to Rs.200 per order, find the
optimal order size.
[10]
10.a) Explain the terms i) rectangular games. ii) types of strategies.
b) Solve the following game graphically where pay off matrix for player A is given below.
[5+5]
1 5 -7 4
2
2 4 9 -3 1
OR
11. Find the shortest path from vertex A to K along arcs joining various vertices lying
between A to K .Length of each path is given.
[10]
B
E
H
A
7
6
5
C
F
I
B
3
4
-
E
6
7
10
H
-
7
10
D
G
J
C
9
7
-
F
7
6
5
I
-
4
3
K
D
3
G
9
J
8
--ooOoo--
This post was last modified on 17 March 2023