Sunday, September 30, 2012
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)
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
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
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
2x1 + x2 < = 1
3x1 + 4x2 > = 4
x1, x2 > = 0
Q7) Solve by using Simplex method
Maximize z = 3x1 + 2x2 + 5x3
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
(a) Minimum cost method
(b) North-West corner rule
(c) VAM method
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.
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
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
30x + 10y > = 240
10x + 10y > = 160
20x + 60y > = 480
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