Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 8th Semester (Eight Semester) 2017-18 NME 051 Operations Research Question Paper
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B.TECH
(SEM?VIII) THEORY EXAMINATION 2017-18
OPERATIONS RESEARCH
T ime: 3 H ours T 0tal M arks: 100
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
2. Any special paper specific instruction.
SECTION A
1. Attempt all questions in brief. 2 x 10 = 20
Explain basic feasible solution of LPP.
What is the condition for degeneracy in LPP?
What do you mean by unbalanced transportation problem?
Define saddle point in game theory.
The monthly demand of the product is 200 units, the holding cost is 2% of the unit
cost, the ordering cost is Rs. 1000 and the unit cost of product is Rs 100. F ind EOQ.
Explain multi channel queuing models.
Write some applications of network techniques.
Explain an unbalanced assignment problem.
Explain pure strategy in game theory.
j. Write the parameters on which EOQ depends.
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SECTION B
2. Attempt any three of the following: 10 x 3 = 30
a. Solve by simplex method:
Maximise: z = 2x + 5y
Subjectedto: x+4y524, x+y:9, 3x+y521
xyEO
b. There are ?ve jobs to be assigned one each to five machines and the associated cost
matrix is given below. Assign the jobs and find out minimum cost.
I II III IV V
A 11 17 8 16 20
B 9 7 12 6 15
C 13 16 25 12 16
D 21 24 17 28 26
E 14 10 12 11 15
c. A machine operator has to perform two operations, turning and threading, on a number
of different jobs. The time required to perform these operations (in minutes) for each
job is known. Determine the order in which the jobs should be processed in order to
minimize the total time required to turn out all the jobs.
Ink Time for turning Time for threading
1 3 8
g 12 10
2 5 9
A 2 6
g 9 3
A 11 1
(1. Why items are stocked in inventory? Explain different types of costs associated with
inventory system.
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e. Explain the following terms:
(i) Queue discipline (ii) Jockeying (iii) Traffic intensity (iv) Balking (V)
Reneging.
SECTION C
Attempt any one part of the following: 10 x 1 = 10
(a) What do you understand from sensitivity analysis in LPP? What is the advantage of
carrying out sensitivity analysis? Give examples,
(b) Solve the following problem by using graphical method or otherwise
Minimize Z= 3X1+2X2
Subjected to 8X1+X2 Z 8, 2X1+X23 6, X1+3X22 6, X1+6X2 2 8, X1, X2 2 0
Attempt any one part of the following: 10 x 1 = 10
(a) What are the methods to optimize a transportation problem? Explain any one of them.
(b) Goods have to be transported from the source $1, $2, 83 to destinations D1, D2, D3. The
transportation cost per unit, capacities of the sources and requirements of the
destinations are given in the following table,
D1 D2 D3 Supply
81 8 5 6 120
$2 15 10 12 80
$3 3 9 10 80
Demand 150 80 50
Determine the transportation schedule so that the cost is minimized,
Attempt any one part of the following: 10 x 1 = 10
(a) Define the following:
(i) Pure strategy (ii) Mixed strategy (iii) Saddle point (iV) Payoff matrix
(V) Two-person Zero-sum game
(b) Reduce the following game by Dominance method and then ?nd out optimal strategies
for both of the players.
Player B
I II III IV V VI
I 4 2 0 2 1 1
E II 4 3 1 3 2 2
3, III 4 3 7 -5 1 2
E IV 4 3 4 ?1 2 2
V 4 3 3 -2 2 2
Attempt any one part of the following: 10 x 1 = 10
(a) What do you understand by simulation? Explain Mounte-Carlo simulation using an
example,
(b) The demand of a particular product is continuous and shows the following distribution
Demand 0 1 2 3 4 5 6 7ormore
Probability 0.02 0.05 0,30 0,27 0.20 0.10 0.06 0.00
Find out the optimum stock level if the cost of shortage is Rs 110 per unit and cost of
holding is Rs 5 per unit, The shortage cost is proportional to both time and quantity
short.
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7. Attempt any one part of the following: 10 x 1 = 10
(a)
(b)
Distinguish between CPM and PERT. Also explain free ?oat and independent ?oat
The customer arrives at a reception counter at an average inter arrival rate of 2
minutes The receptionist in duty takes an average of one minute per customer.
(i) What is the chance that a customer will straight way meet the receptionist?
(ii) What is the average queue length?
(iii) What is the average no. of customers in the system?
(iV) What is the average waiting time of customers in the queue?
(V) Suppose management wants to keep a second receptionist when the average
waiting time of an arrival exceeds 15 minutes Find what should be the average
inter-arrival time to justify a second receptionist?
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This post was last modified on 30 January 2020