Total No. of Questions 10] [Total No. of Pages 03
M.Sc. DEGREE EXAMINATION, MAY 2018
Second Year
STATISTICS
Operations Research
Time 3 Hours Maximum Marks :70
Answer any five questions.
All questions carry equal marks.
(5×14=70)
Q1) Define operations research. Explain the significance of O.R. models.
Use simplex method to solve the following L.P.P. Minimize x−3y;
Subject to the conditions x y 300; x − 2y 200;2x y x1x2 0 .
Q2) Use Big-M method to solve the following L.P.P. Minimize 2x1+9x2+x3;
subject to the conditions 1 2 3 x 4x 2x 1 2 3 3x x 2x 1 2 3 x x x 0 .
Determine the dual and solve the following L.P.P. Maximize 4x1+2x2;
subject to the conditions 1 2 x − 2x 1 2 x 2x 1 2 x − x 1 2 x x 0.
Q3) Distinguish between deterministic and stochastic models in inventory.
Annual demand for an item is 500 units, ordering cost is Rs.18 per order.
Inventory carrying cost is Rs.15 per unit per year relationship between price
and quantity ordered is as follows:
Quantity ordered 1 to 15 16 to 149 150 to 549 550 over
Price per unit 10 9 8.75 8.50
Specify optimal order quantity and the corresponding price of this item.
Q4) Discuss in brief the replacement procedure for items that deteriorate with
time.
The yearly cost of two machines A and when money value is neglected is
shown below. Find their cost patterns if money is worth 10 percent per year
and hence find which machine is more economical.
Year 1 2 3
Machine A 1800 1200 1400
Machine B 2800 1200 1400
Q5) Explain various quantitative methods which are useful for decision-making
under uncertainty.
Solve the following game by dominance method.
Player B
Player A
15 2 3
6 5 7
7 4 0




Q6) Explain the difference between pure strategy and mixed strategy.
Solve the following game by Linear programming approach.
Player B
Player A
9 1 4
0 6 3
5 2 8





Q7) Brief explain the important characteristics of queuing system.
The mean arrival rate to a service center is 3 per hour. The mean service time
is found to be 10 min per service. Assuming Poisson arrival and exponential
service time, find
Probability of two units in the system.
ii) Expected no. of units in the queue.
iii) Expected time in minutes that customer has to spend in the system.
Q8) Write a short note on queue and its applications.
In a railway marshalling yard, goods trains arrive at a rate of 30 trains per
day. Assume that the inter arrival time follows an exponential distribution
and the service time distribution is also exponential with an average of 36
minutes. Calculate
The probability that the yard is empty.
ii) Average queue length assuming that the line capacity of the yard is 9
trains.
Q9) What is the difference between PERT and CPM.
Consider the following data for the activities of a project:
Activity A B C D E F
Predecessor A A C E
Duration (in days) 2 3 4 6 2 8
Draw the network and find critical path and project duration.
Q10)a) Explain the uses of CPM/PERT.
Following are the activities of a project.
Activity A B C D E F G H I
Proceeding A A C D B F G
a 4 1 6 2 5 3 3 1 4
m 7 5 12 5 11 6 9 4 19
b 16 15 30 8 17 15 27 7 28
Draw the network diagram.
ii) Find out critical path and project duration.
iii) If project manager wishes to be 99% sure that the project is completed on
30th March, 2017, when should he start the project work?