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Reg.
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER MCA DEGREE EXAMINATION, AUG 2017
RLMCA108: OPERATIONS RESEARCH
Max. Marks: 60. Duration: 3 Hours
PART A
Answer all questions. Three marks each.
1. Define: Basic solution and Feasible solution
2. Solve graphically the LPP
Maximise subject to 10, 15
Where 0
3. Find an initial basic feasible solution by North West corner method.
D E F G Availability
A 11 13 17 14 250
B 16 18 14 10 300
C 21 24 13 10 400
Demand 200 225 275 250
4. State the Maximin Minimax principle.
5. Write symbolic representations of a queuing model and mention the meaning of each
symbol.
6. What are the steps in the methodology of simulation?
7. State the Fundamental theorem of duality
8. How do simulated sampling method (Monte-Carlo method) used to evaluate the value of

PART B
Answer one question from each module. Six marks each.
MODULE I
9. Suppose that you are investing Rs. in a combination of two shares A and B .
The maximum investment allowed in either share is Rs. 75,000/-. Share A has an average
rate of return of 10% and risk 40% whereas Share B has an average rate of return of 20%
and risk 90%. You are not ready to accept rate of return below 12% and risk above 60%.
Formulate this as a LPP and solve it graphically.
12. Prove that the dual of the dual is the Primal problem.
MODULE III
13. Use Vogel's approximation method to obtain an IBFS of the transportation problem
Warehouse
W1 W2 W3 Supply
Factory
F1 16 20 12 200
F2 14 8 18 160
F3 26 24 16 90
Demand 180 120 150
14. The Head of the Department has 5 jobs D and E and 5 subordinates Y
and Z. The number of hours each person would take to perform each job is as follows.
How should the jobs be allocated to minimize the total time?
V W X Y Z
A 3 5 10 15 8
B 4 7 15 18 8
C 8 12 20 20 12
D 5 5 8 10 6
E 10 10 15 25 10
MODULE IV
15. Solve the following 2x2 game graphically.
Player II
B1 B2 B3 B4
Player
I
A1 2 1 0
A2 1 0 3 2
16. Two firms are competing for business under the condition so that one firm's gain is
another firm's loss. Firm payoff matrix is given below:
Firm B
No advertising Medium
advertising
High
advertising
Firm
A
No advertising 10 5
Medium advertising 13 12 15
High advertising 16 14 10
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Suggest optimum strategies for the two firms and the net outcome thereof.
MODULE V
17. Customers arrive at a one-man barber shop according to a Poisson process with a mean
inter arrival time of 12 minutes. On the average, customers spend 10 minutes in the
barber's chair.
a. What is the expected number of customers in the shop?
b. What is the expected number of customers in the queue?
c. What is the probability of a customer walking directly to the barber's chair
without waiting in the queue?
d. What is the average time customers spend in the queue?
e. What is the average time customers spend in the shop?
f. What is the probability that more than 3 customers are in the shop?
18. Patients arrive at a clinic according to a Poisson distribution at a rate of 30 patients per
hour. The waiting room does not accommodate more than 14 patients. The examination
time for a patient is exponentially distributed with a mean rate of 20 per hour.
a. What is the effective arrival rate of patients at the clinic?
b. What is the expected number of patients in the waiting hall?
c. What is the expected number of patients in the clinic?
d. What is the probability of a patient walking directly to the doctor's room without
waiting?
e. What is the expected waiting time of a patient in the clinic?
f. What is the expected waiting time of a patient in the waiting hall?
MODULE VI
19. a. What are the advantages of simulation?
b. What are the elements of simulation?
20. Customers arrive at a milk booth for the required service. Assume that the inter-arrival
service times are constant and given by 1.8 and 4 time units, respectively. Simulate the
system by hand computations for 14 time units.
a. What is the average waiting time per customer?
b. What is the percentage idle time of the facility? (Assume that the starts at