This document is a 4-page examination for an Operations Research course containing 7 questions worth a total of 100 marks. Students are asked to answer any 5 of the 7 questions, which cover topics such as linear programming, transportation problems, assignment problems, sequencing problems, queuing theory, simulation, game theory, and replacement problems. Questions involve solving models mathematically as well as discussing concepts in operations research.

1. Page 1 of 4
Term End Examination - November 2012
Course : MEE437 - Operations Research Slot: B2+TB2
Class NBR : 2713 / 2708 / 5569 / 2710 / 3562 / 5568
Time : Three Hours Max.Marks:100
Note:
1. Use of Standard Normal and Random Number Tables are permitted
2. Graph sheet is to be provided
Answer any FIVE Questions
(5 X 20 = 100 Marks)
1. a) Apply the graphical method to solve the LPP:
Max Z = 5x1 + 8x2
Subject to 15x1+10x2 ≤ 180
10x1+20x2 ≤ 200
15x1+20x2 ≤ 210
and x1 , x2≥ 0.
[5]
b) Solve the following using Simplex method
Max Z = 15x1 + 6x2 +9x3 + 2x4
Subject to 2x1 + x2 +5x3 + 6x4 ≤ 20
3x1 + x2 +3x3 + 25x4 ≤ 24
-7x1-x4 ≥ 70
and x1 , x2, x3 , x4≥ 0.
[15]
2. a) Solve the transportation problem (use VAM) and find the optimal solution using
MODI method.
Origin
Destination
Supply (units)D1 D2 D3
A 5 6 9 100
B 3 5 10 75
C 6 7 6 50
D 6 4 10 75
Demand
(units)
70 80 120
[15]

2. Page 2 of 4
b) Solve the assignment problem
A B C D
I 1 4 6 3
II 9 7 10 9
III 4 5 11 7
IV 8 7 8 5
[5]
3. a) Find the optimum sequence for the following sequencing problem. Also find the
minimum total elapsed time and idle time on the machines M1 and M2.
JOBS
A B C D E F G H
M1 14 26 17 11 9 26 18 15
M2 21 15 16 21 22 12 13 25
[10]
b) The following table lists the jobs of a network along with their time estimates
Jobs 1-2 1-3 2-4 3-4 4-5 3-5
Optimistic time 2 9 5 2 6 8
Most likely time 5 12 14 5 6 17
Pessimistic time 14 15 17 8 12 20
i) Draw the network
ii) Calculate the length and variance of the critical path
iii) Find the probability that the project will be completed within 30 days.
[10]

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4. a) A manufacturer has to supply his customer with 600 units of his products per year.
Shortage are not allowed and storage cost amounts to 60 paise per unit per year.
The set up cost is Rs.80.
Find i) the economic order quantity
ii) the minimum average yearly cost
iii) the optimum number of orders per year
iv) the optimum period of supply per optimum order
[10]
b) The demand for an item in a company is 18,000 units per year, and the company
can produce the item at a rate of 3000 per month. The cost of one set up is
Rs. 500 and the holding cost of one unit per month is 15 paise. The shortage cost
of one unit is Rs.20 per month. Determine the optimum manufacturing quantity
and the number of shortages. Also determine the manufacturing time and time
between set-ups.
[10]
5. a) Cars arrive at a petrol pump, having one petrol unit, in Poisson fashion with an
average of 10 cars per hour. The service time is distributed exponentially with a
mean of 3 minutes.
Find i) average number of cars in the system ii) average waiting time in the
Queue iii) average Queue length iv) the probability that the number of cars in the
system is 2.
[15]
b) Write the different steps involved while solving a simulation problem [5]
6. Using dominance solve the game whose payoff matrix is given by
PLAYER K
I II III IV
A 18 4 6 4
PLAYER L B 6 2 13 7
C 11 5 17 3
D 7 6 12 2

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7. a) The maintenance cost and resale value per year of a machine whose purchase price
is Rs.7000 is given below:
Year Maintenance Cost (Rs) Resale Value (Rs)
1 900 4000
2 1200 2000
3 1600 1200
4 2100 600
5 2800 500
6 3700 400
7 4700 400
8 5900 400
When should the machine be replaced?
[15]
b) What is meant by replacement problem? Discuss the various types of replacement
problems.
[5]
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