(AUTONOMOUS)
B. Tech VII Semester Supplementary Examinations, May 2018
(Regulations: VCE-R11/R11A)
OPERATIONS RESEARCH
(Common to Computer Science and Engineering, Information Technology
Mechanical Engineering)
Date: 28 May, 2018 AN Time: 3 hours Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
Unit I
1. Discuss about the limitations of Operation Research. 6M
In the production of 2 types of toys, a factory uses 3 machines B and C. The time
required to produce the first type of toy is 6 hours, 8 hours and 12 hours in machines B
and C respectively. The time required to make the second type of toy is 8 hours, 4 hours
and 4 hours in machines B and C respectively. The maximum available time (in hours)
for the machines C are 380, 300 and 404 respectively. The profit on the first type of
toy is 5 dollars while that on the second type of toy is 3 dollars. To find the number of
toys of each type that should be produced to get maximum profit, formulate the problem
as an LPP.
9M
2. Solve the following LPP by Big-M method:
Max
1 2
Z x
Subject to
1 2
1 2
1 2
3 3
4 3 6
2 4
x x
x x
x x



1 2 and x x 0
15M
Unit II
3. Solve the assignment problem represented by the following matrix:
Job
Typist P Q R S T
A 85 75 65 125 75
B 90 78 66 132 78
C 75 66 57 114 69
D 80 72 60 120 72
E 76 64 56 112 68
15M
4. Find the optimum solution to the following transportation problem:
Distribution Centre
D1 D2 D3 D4 Supply
Plant
P1 19 30 50 12 7
P2 70 30 40 60 10
P3 40 10 60 20 18
Requirement 5 8 7 15
15M
Cont…2

Unit III
5. There are four jobs each of which has to go through the machines Mi, in the order
M1, M2,…, M6. Processing times are given below.
Machine(i)
Jobs(j) M1 M2 M3 M4 M5 M6
J1 20 10 9 4 12 27
J2 19 8 11 8 10 21
J3 13 7 10 7 9 17
J4 22 6 5 6 10 14
Determine a sequence for these four jobs which minimizes the total elapsed time, also find
the total elapsed time.
15M
6. Define queue. Briefly explain queuing system and their characteristics. 9M
A self-service store employs one cashier at its counter. Nine customers arrive on an
average every 5 minutes while the cashier can serve 10 customers in 5 minutes.
Assuming Poisson distribution for arrival rate and exponential distribution for service
time, find:
i. Average number of customer in the system
ii. Average number of customer in the queue or average queue length
iii. Average time a customer spends in the system
iv. iv. Average time a customer waits before being served
6M
Unit IV
7. Justify the superiority of Group replacement policy over individual replacement policy. 3M
The mortality of an electronic tube used in the computer is given below:
Period 1 2 3 4 5
Age interval
of failures
0 200 201 400 401 600 601 800 801 1000
Probability of
failure
0.10 0.26 0.35 0.22 0.07
If the tubes are group replaced, the cost of replacement is Rs.15/- per tube. Replacement
of individual tubes those fail in service, cost Rs.60/- per tube. How frequently the tubes
be group-replaced?
12M
8. What are various inventory-related costs? 4M
The production rate of a particular item is 100 per day and the demand is 420 per week.
The setup cost is Rs.80/- and the holding cost is Rs.2.184 per unit per year. Find the
optimal run size and corresponding total variable costs.
11M
Unit V
9. Explain Minimax and Maximin principle used in theory of games. 6M
Use dominance principle to reduce the following game to 2 X 2 games and hence solve
it:
3 5 4 2
5 6 2 4
2 1 4 0
3 3 5 2






9M
10. Explain the characteristics of Dynamic Programming. 5M
Solve the following using dynamic programming:
2 2 2
1 2 1 2 Min Z .... . . . ... y y yn S T C y y yn c yi i n
10M