LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – MATHEMATICS

FIFTH SEMESTER – April 2009
MT 5507 / 5504 – OPERATIONS RESEARCH
Date & Time: 17/04/2009 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL Questions (10 x 2 = 20)
 Write down any two uses of Operations Research.
 Define Slack variables.
 Which is the necessary and sufficient condition for the transportation problem to have
a feasible solution?
 Describe a traveling salesman problem.
 What is meant by mixed strategy?
 What is the value of the game?
 Define Total float
 Explain: Minimal Spanning tree problem?
 Give any two reasons for maintaining inventory
 Define Recorder level.
SECTION B
Answer ANY FIVE Questions. (5 x 8 = 40)
 Solve the following Linear Programming Problem by graphical method
Maximize Z = 5x_{1 }+ 8x_{2}
Subject to:
15x_{1 }+ 10x_{2 }≤ 180
10x_{1 }+ 20x_{2 }≤ 200
15x_{1 }+ 20x_{2 }≤ 210
and x_{1}, x_{2 }≥ 0
 Use simplex method to solve the following LPP
Maximize Z = 4x_{1 }+ 10x_{2}
Subject to:
2x_{1 }+ x_{2 }≤ 50
2x_{1 }+ 5x_{2 }≤ 100
2x_{1 }+ 3x_{2 }≤ 90
and x_{1}, x_{2 }≥ 0
 Find the initial basic feasible solution for the following transportation problem
D_{1}  D_{2}  D_{3}  D_{4}  Supply  
S_{1}  21  16  25  13  11 
S_{2}  17  18  14  23  13 
S_{3}  32  27  18  41  19 
Demand  6  10  12  15 
 Write the algorithm for solving Assignment problem.
 Solve the following game using dominance property.
I  II  III  Row mini.  
I  1  7  2  1 
II  6  2  7  2 
III  6  1  6  1 
Column max.  6  7  7 
 Draw the network for the project whose activities with their predecessor relationships
are given below:
A, C, D can start simultaneously; E >B, C; F, G >D; H, I > E ,F ; J >I, G ;
K > H; B > A.
 The annual demand of a product is 10,000 units, each unit cost Rs.100 if orders
placed in quantities below 200 units but for orders of 200 or above, the price is Rs.95,
the annual inventory holding cost is 10% of the value of the item, and the ordering
cost is Rs.5 per order. Find the economic lot size.
 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 shortage. Also determine the manufacturing time and time between setups.
SECTION C
Answer ANY TWO Questions. (2 x 20 = 40)
 Solve the following Linear Programming Problem by Dual Simplex method
Minimize Z = x_{1 }+ x_{2}
Subject to:
2x_{1 }+ x_{2 }≥ 2
x_{1 }– x_{2 }≥ 1
and x_{1}, x_{2 }≥ 0
 (a) Solve the following transportation problem using Least Cost Method to find the
Initial Basic Feasible solution.
A_{1}  A_{2}  A_{3}  A_{4}  A_{5}  Supply  
B_{1}  4  1  2  6  9  100 
B_{2}  1  4  7  3  8  120 
B_{3}  7  2  4  7  7  120 
Demand  40  20  70  90  90 
.
(b)Solve the following traveling sales man problem
M_{1}  M_{2}  M_{3}  M_{4}  M_{5}  
J_{1}  9  22  58  11  19 
J_{2}  43  78  72  50  63 
J_{3}  41  28  91  37  45 
J_{4}  74  42  27  49  39 
J_{5}  36  11  57  22  25 
(10 + 10)
 (a) Solve the following game graphically
B_{1}  B_{2}  B_{3}  B_{4}  
A_{1}  1  0  4  1 
A_{2}  1  1  2  5 
(b) In a game of matching points with 2 players suppose A wins one unit value when
there are 2 heads, wins nothing when there are 2 tails, and loses ½ unit value when
there are 1 head and 1 tail. Determine the payoff matrix, the best strategy for each
player and the value of the game. (10+10)
22 (a) Draw the network, determine the critical path , project duration and the total float for the
following activities .
Activity  12  23  34  37  45  47  56  67 
Duration  3  4  4  4  2  2  3  2 
(b) ABC manufacturing company purchases 9,000 parts of a machine for its annual
requirement, ordering one month’s usage at a time. Each part costs Rs.20.
The ordering cost per order is Rs.15, and the carrying charges are 15% of the
average inventory per year.
You have been asked to suggest a more economical purchasing policy for the
company. What advice would you offer and how much would it save the company
per year? (10+10)
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