Q3➡| NTA UGC NET December 2019 Consider the following statements with respect to duality in LPP: (a) The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself. (b) If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution. (c) If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all. Which of the statements is (are) correct?
Q4➡| NTA UGC NET December 2019 A basic feasible solution of an mXn Transportation-Problem is said to be non-degenerate, if basic feasible solution contains exactly____number of individual allocation in ___positions
Q8➡| NTA UGC NET JUNE 2018 The following LPP Maximize z=100x1+2x2 +5x3 Subject to 14x1+x2 −6x3 +3x4 =7 32x1 +x2 −12x3 ≤10 3x1 −x2 −x3 ≤0 x1 , x2 , x3 , x4 ≥ 0 has
Q9➡| NTA UGC NET November 2017 Paper -3 Which of the following is a valid reason for causing degeneracy in a transportation problem ? Here m is no. of rows and n is no. of columns in transportation table
i ➥ When the number of allocations is m+n−1.
ii ➥ When two or more occupied cells become unoccupied simultaneously.
iii ➥ When the number of allocations is less than m+n−1.
iv ➥ When a loop cannot be drawn without using unoccupied cells, except the starting cell of the loop.
Q10➡| NTA UGC NET November 2017 Paper -3 Consider the following LPP : Max Z = 15x1 + 10x2 Subject to the constraints 4x1 + 6x2 ≤ 360 3x1 + 0x2 ≤ 180 0x1 + 5x2 ≤ 200 x1, x2 / 0 The solution of the LPP using Graphical solution technique is :
Q11➡| NTA UGC NET November 2017 Paper -3 Consider the following LPP : Min Z = 2x1 + x2 + 3x3 Subject to : x1 − 2x2 + x3 ≥ 4 2x1 + x2 + x3 ≤ 8 x1 − x3 ≥ 0 x1, x2, x3 ≥ 0 The solution of this LPP using Dual Simplex Method is :
i ➥ x1=0, x2=0, x3=3 and Z=9
ii ➥ x1=0, x2=6, x3=0 and Z=6
iii ➥ x1=4, x2=0, x3=0 and Z=8
iv ➥ x1=2, x2=0, x3=2 and Z=10
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Answer: I (Marks to all ) Explanation: Upload Soon
Q15➡| NTA UGC NET January 2017 Paper -3 At which of the following stage(s), the degeneracy do not occur in transportation problem ? (m, n represents number of sources and destinations respectively) (1) While the values of dual variables ui and vj cannot be computed. (2) While obtaining an initial solution, we may have less than m + n – 1 allocations. (3) At any stage while moving towards optimal solution, when two or more occupied cells with the same minimum allocation become unoccupied simultaneously. (4) At a stage when the no. of +ve allocation is exactly m + n – 1.
Q18➡| NTA UGC NET August 2016 Paper -3 The region of feasible solution of a linear programming problem has a _ property in geometry, provided the feasible solution of the problem exists.
Q19➡| NTA UGC NET August 2016 Paper -3 Consider the following statements: (1) Revised simplex method requires lesser computations than the simplex method. (2) Revised simplex method automatically generates the inverse of the current basis matrix. (3) Less number of entries are needed in each table of revised simplex method than usual simplex method. Which of these statements are correct?
Q21➡| NTA UGC NET December 2015 Paper -3 A basic feasible solution of a linear programming problem is said to be __ if at least one of the basic variables is zero.
Q22➡| NTA UGC NET December 2015 Paper -3 Consider the following conditions: (a)The solution must be feasible, i.e. it must satisfy all the supply and demand constraints. (b)The number of positive allocations must be equal to m+n-1, where m is the number of rows and n is the number of columns. (c)All the positive allocations must be in independent positions. The initial solution of a transportation problem is said to be non-degenerate basic feasible solution if it satisfies:
Q23➡| NTA UGC NET December 2015 Paper -3 Consider the following transportation problem: The transportation cost in the initial basic feasible solution of the above transportation problem using Vogel’s Approximation method is:
Q24➡| NTA UGC NET June 2015 Paper -3 In the Hungarian method for solving assignment problem, an optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost is equal to the number of:
Q25➡| NTA UGC NET June 2015 Paper -3 Given the following statements with respect to linear programming problem: S1 : The dual of the dual linear programming problem is again the primal problem S2 : If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution. S3 : If either the primal or dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal. Which of the following is true?
Q26➡| NTA UGC NET June 2015 Paper -3 Consider the following transportation problem: The initial basic feasible solution of the above transportation problem using Vogel’s Approximation Method (VAM) is given below: The solution of the above problem.
