Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 2nd Sem (Second Semester) Regulation-R17 2019 December 842AD Operations Research Previous Question Paper
R17
Code No: 842AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA II Semester Examinations, December - 2019
OPERATIONS RESEARCH
STime: 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) Write a short notes on Characteristics of Operation Research.
[5]
b) Define the following terms in the context of sequencing problem
i) Total elapsed time
ii) Idle time, processing order.
[5]
c) Write about the customer behavior in the queue.
[5]
d) Define inventory. What are the advantages and disadvantages of having
Inventories?
[5]
e) Define i) Pure strategy ii) Mixed Maxmin principle, saddle point, value of the game.
[5]
PART - B
5 ? 10 Marks = 50
2. a) A small manufacturer employs 5 skilled men and 10 semi-skilled men for making a
product in two qualities : a deluxe model and an ordinary model. The production of a
deluxe model requires 2- hour work by a skilled man and a1-hour work by a semi-skilled
man. The ordinary model requires 2-hour work by a skilled man and 3-hour work by a
semi-skilled man. According to worker union's rules, no man can work more than 8
hours per day. The profit of the deluxe model is Rs. 1000 per unit and that of the
ordinary model is Rs. 800 per unit. Formulate a linear programming model for this
manufacturing situation to determine the production volume of each model such that the
total profit is maximizing.
b) Solve the following LP problem graphically
Minimize Z = 45 X1 + 55 X2
Subject to
X1 + 2 X2 30
2X1 + 3 X2 80
X1 - X2 8
X1 and X2 0.
[10]
OR
3.
A company has three cement factories located in cities 1, 2, 3 which supply cement to
four projects located in towns 1, 2, 3, 4. Each plant can supply 6, 1, 10 truckloads of
cement daily respectively and the daily cement requirements of the projects are
respectively 7, 5, 3, 2 truck loads. The transportation costs per truck load of cement (in
S hundreds of rupees) from each plant to teach project site are as follows:
Project sites
1
2
3
4
Factories
1
2
3
11
7
2
1
0
6
1
3
5
8
15
9
Determine the optimal distribution for the company so as to minimize the total
transportation cost.
[10]
4.
Find the sequences that minimizes the total elapsed time required to complete the
following tasks. Each task is processed in any two of the machines A, B and C in any
order
[10]
Task
OR
5.
A fleet owner finds from his past records that the costs per year of running a truck whose
purchase price is Rs. 6000 are as given below:
Year
1
2
3
4
5
6
7
8
Running costs
(in Rs.)
1500 1600 1800 2100 2500 2900 3400 4000
Resale value
(in Rs.)
3500 2500 1700 1200 800 500
500
500
Determine at what age is the replacement due?
[10]
6.
Arrival rate of telephone calls at a telephone booth are according to Poisson distribution
with an average time of 9 minutes between two consecutive arrivals. The length of
telephone call is assumed to be, with mean 3 minutes.
a) Determine the probability that a person arriving at the booth will have to wait.
b) Find the average queue length that is formed from time to time.
c) The telephone company will install a second booth when convinced that an arrival
would aspect to have to wait at leave four minutes for the phone. Find the increase in
flow rate of arrivals which will justify a second booth.
d) What is the probability that an arrival will have to wait for more than 10 minutes
before the phone is free?
[10]
OR
7.
The arrival rate of customers at a banking customer follows Poisson distribution with a
mean of 45 per hour. The service rate of the counter clerk also follows Poisson
distribution with a mean of 60 per hour.
a) What is the probability of having 0 customer in the system?
b) What is the probability of having 5 customers in the system?
S c) What is the probability of having 12 customers in the system?
d) Find Lq, Ls
[10]
8.
The demand of a bought out item in a store is 12,000 units per year. The carrying cost is
Rs. 2 per unit per year and the ordering cost is Rs. 600 per order. The storage cost is Rs.
10 per unit per year. Find the EOQ and the corresponding number of orders per year, the
maximum inventory.
[10]
OR
9.
A manufacturer of engines is required in purchase 2,400 castings per year. The
requirements are assumed to be fixed and known. The manufacturer is given a lower
price for quantity purchased within certain ranges. The problem is to determine the
optimal purchase quantity. Time period T = 12 months, total demand R = 2, 400 units,
I = 2%, K11 = Rs. 10 for 0 q < 500, K12 = Rs. 925 for q 500.
[10]
10. Solve the following game by using the principle of dominance:
[10]
Player B
I
II
III
IV
V
VI
1
4
2
0
2
1
1
Player A 2
4
3
1
3
2
2
3
4
3
7
-5
1
2
4
4
3
4
-1
2
2
5
4
3
3
-2
2
2
OR
11.
An oil company has 8 units of money available for exploration of three sites. If oil is
present at a site, the probability of finding it depends upon the amount allocated for
exploiting the site, as given below
Units of money allocated
0
1
2
3
4
5
6
7
8
Site 1
0.0
0.0
0.1
0.2
0.3
0.5
0.7
0.9
1.0
Site 2
0.0
0.1
0.2
0.3
0.4
0.6
0.7
0.8
1.0
Site 3
0.0
0.1
0.1
0.2
0.3
0.5
0.8
0.9
1.0
The probability that the oil exists at sites 1,2 and 3 is 0.4, 0.3 and 0.2 respectively. Find
the optimal allocation of money.
[10]
---ooOoo---
This post was last modified on 17 March 2023