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1½×10=15
Total No. of Questions : 11
[Total No. of Printed Pages : 8
MN-465
M.A./M.Sc. IIIrd Semester (Reg./Pvt./ATKT)
Examination, 2023-24
Maths
Operations Research-I
Paper - VIII
Time : 3 Hours]
[Maximum Marks : Reg. 85 Pvt. 100
Note :- Attempt all questions.
SECTION - 'A'
Objective Type Questions
1.
Choose the correct answer :
(i) The origin of operation research is related to :
- (a) First world war
- (b) Second world war
- (c) Third world war
- (d) None of these
(ii) The journal "Operation" was published for the first time in
- (a) 1940
- (b) 1959
- (c) 1963
- (d) 1969
(iii) Which one is not a phase of OR methods
- (a) Formulation
- (b) Testing the model
- (c) Take expert opinion
- (d) Maintenance of the solution
(iv) Which is not a characteristic of a good model
- (a) Intraflexible
- (b) Non-predictive
- (c) Law of parsimony
- (d) Not take much time
(v) LPP converts the following parts
- (a) Objective function
- (b) Subject to constraints
- (c) Feasibility constraints
- (d) All above
(vi) Graphical method can solve L.L.P easily
- (a) 2 variables
- (b) 3 variables
- (c) N variables
- (d) None of these
(vii) Condition for optimum solution in simplex method
- (a) Zj - Cj ≤ 0
- (b) Zj - Cj > 0
- (c) Zj - Cj < 0
- (d) Zj - Cj ≥ 0
(viii) In simplex method the set of constrains can be write in the form Ax=b by using
- (a) Stock variable
- (b) Surplus variable
- (c) Artificial variable
- (d) All of above
(ix) Dual of dual is :
- (a) Dual
- (b) Primal
- (c) Tripel
- (d) Not defined
(x) If solution of a primal problem is infeasible then the solution of dual problem is :
- (a) Optimum
- (b) Unbounded
- (c) Infeasible
- (d) Not defined
10.
Solve graphically the following problem
Max (z) = 3x₁ + 2x₂
Subject to
2x₁ - x₂ ≥ 2
x₁ + 2x₂ ≤ 8
x₁, x₂ ≥ 0
OR
Solve the following LPP by simplex method
Max (z) = 2x₁ + 4x₂ + x₃ + x₄
subject to
x₁ - 3x₂ + x₄ ≤ 4
2x₁ + x₂ ≤ 3
x₁ + 4x₃ + x₄ ≤ 3
x₁, x₂, x₃, x₄ ≥ 0
OR
Use the degeneracy technique to solve the following LPP
Min (z) = x₁ + x₂
subject to
2x₁ + x₂ ≥ 4
x₁ - 7x₂ ≥ 7
x₁, x₂ ≥ 0
SECTION - 'B'
Short Answer Type Questions
5×5=25
2.
Define operation Research.
3.
Write the advantages of a model.
OR
Describe any five characteristic of operation research.
OR
Describe the necessity of duality.
4.
Discuss the main steps to formulate a problem as alinear programming problem.
OR
Write the limitations of graphical method.
5.
Define general linear programming problem.
OR
Describe the problem of degeneracy.
6.
Obtation the dual of the following problem
Min (z) = 2x₁ + 3x₂ + 4x₃
subject to
2x₁ + 3x₂ + 5x₃ ≥ 2
3x₁ + x₂ + 7x₃ = 3
x₁ + 4x₂ + 6x₃ ≤ 5
x₁, x₂ ≥ 0 is unrestricted
SECTION - 'C'
Long Answer Type Questions
9×5=45
7.
Discuss the scope of operations research.
OR
Describe the development of operations research.
8.
Write the phases of operations research.
OR
Write a short note on models in OR.
9.
A manufacturer of a line of patent medicines is preparing a production plan of medicines A and B. There are sufficient ingredients available to make 20000 bottles of A and 40000 bottles of B but there are only 45000 bottles into which either of the medicines can be put. Furthermore is takes 3 hours to prepare enough material to fill 1000 bottles of A, it takes one hour to prepare enough material to fill 1000 bottles of B ad there are 66 hours available for this operations. The profit is Rs. 8/- per bottle of A and Rs. 7/- per bottle of B. Formulate this problem as a linear programming problem.
11.
Give the dual of the following problem
Min (z) = x₁ + 5x₂
subject to
3x₁ + 4x₂ ≤ 6
x₁ + 3x₂ ≤ 2
x₁, x₂ ≥ 0
OR
State and prove the fundamental theorem of duality in L.P.P.