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Roll No.
.......................
Total No. of
Questions : 13] [Total
No. of Pages : 04
Paper ID [A0224]
(Please fill this Paper ID in OMR Sheet)
BCA (504) (Old/S05) (Sem. - 5th)
OPERATION RESEARCH
Time : 03
Hours Maximum
Marks : 75
Instruction to
Candidates:
1) Section-A is Compulsory.
2) Attempt any Nine questions
from Section-B.
Section - A
Q1) (15
× 2 = 30)
a) Define Operations research.
b) Feasible solution.
c) List the phases in solving an OR problem.
d) Degeneracy in linear programming problem.
e) Any two limitations of Operations research.
f) Decision making under uncertainty.
g) Unbalanced transportation problem.
h) Minimax criterion.
i) Difference between linear programming and integer programming.
j) Write the dual of following Linear programming problem
Maximize z = 2x1 + x2 – 3x3 + 5x4
Subject to
x1 + 7x2 + 3x3 + 7x4 < = 46
3x1 – x2 + x3 + 2x4 < = 8
2x1 + 3x2 – x3 + x4 < = 10
k) Any two differences between Transportation and assignment model.
l) List two applications of Dynamic programming.
m) Why do we
apply heavy penalty to artificial variable in the objective function for solving
linear programming problem?
n) What does
the difference of smallest and second smallest element signifies in case of
solving Transportation problem with VAM method?
o) Expected
opportunity loss criterion of decision making.
Section - B
(9 × 5 = 45)
Q2) What is the role of
Operation research in decision making? Explain.
Q3) Explain the following
types of models (a) Iconic (b) Analogue.
Q4) Discuss briefly the
various phases of solving an OR problem.
Q5) Solve Graphically
Maximize z = x1 + x2/2
Subject to
3x1 + 2x2< = 12
5x1 < = 10
x1 + x2< = 8
–x1 + x2 > = 4
Q6) Solve the following
problem by using big M technique
Maximize z = 3x1 + 2x2
Subject to
2x1 + x2 < = 1
3x1 + 4x2 > = 4
x1, x2 > = 0
Q7) Solve by using Simplex
method
Maximize z = 3x1 + 2x2 + 5x3
Subject to:
x1 + x2 + x3 < = 9
2x1 + 3x2 + 5x3 < = 30
2x1 – x2 – x3 < = 8
J-8782 - 2 -
Q8) Find the initial basic
feasible solution of the following transportation problem
by
(a) Minimum
cost method
(b)
North-West corner rule
(c) VAM
method
To Supply
12 17 14 15
From 13 13 11
18
15 14 17 17
11 16 12 14
Demand 17 29
18
Q9) Four different jobs are
to be done on four different machines. The following table indicates the cost
of producing job I on machine j. Changeover cost is very high. Assign the jobs
to different machines so that the total cost is minimized.
Machines
1 2 3 4
1 5 7 11 6
Jobs 2 8 5 9
6
3 4 7 10 7
4 10 4 8 3
Q10) A newspaper boy has the
following probabilities of selling a magazine. No. of copies sold Probability
10 0.10
11 0.15
12 0.20
13 0.25
14 0.30
Cost of a
copy is 30 paise and sales price is 50 paise. He cannot return the unsold
copies. How many copies should he order?
Q11) Explain with example, how
decision trees are helpful in decision-making? What are the limitations of
decision tree approach?
Q12) What is dynamic
programming? Explain some salient characteristics of this approach that
distinguish it from other techniques of Operations research.
Q13) Solve the following
Graphically
Minimize z = 60x + 40y
Subject to
30x + 10y > = 240
10x + 10y > = 160
20x + 60y > = 480
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