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Math Chapter Wise Linear Programming Problems English Bihar (TRE 2.0)-2023

Q67541.The optimal value of the objective function is attained at the points

Aon X -axis Bon Y-axis Con the corner points of the feasible region DMore than one of the above ENone of the above

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Math Chapter Wise Linear Programming Problems English Bihar (TRE 2.0)-2023

Q67542.The point which does not lie in the half-plane 2x + 3y -12 < 0 is

A(2, 3) B(–2, 3) C(1, 2) DMore than one of the above ENone of the above

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Math Chapter Wise Linear Programming Problems English Bihar (TRE 1.0) -2023

Q67543.The Linear Programming Problem Maximize z = x1 + x2 subject to x1 + 2x2 ≤ 20 x1 + x2 ≤ 15 x2 ≤ 6 x1, x2 ≥ 0

AHas exactly one optimum solution BHas more than one optimum solution CHas no solution DMore than one of the above ENone of the above

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Math Chapter Wise Linear Programming Problems English Bihar (TRE 1.0) -2023

Q67544.The dual of the linear programming problem: Minimize CT x subject to Ax ≥ b and x ≥ 0 is

AMaximize bT w subject to AT w ≥ c and BMaximize bT w subject to AT w ≤ c and CMaximize bT w subject to AT w ≤ c and w is unrestricted. DMore than one of the above ENone of the above

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Math Chapter Wise Linear Programming Problems English Bihar (TRE 1.0) -2023

Q67545.A transportation problem is

Adual problem Bnon-linear programming problem Cspecial case of linear programming problem DMore than one of the above ENone of the above

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Math Chapter Wise Linear Programming Problems English KVS PGT 2023

Q67546.If the corner points of the LPP, Z = 13x - 15y subject to the constraints x + y ≤7, 2x - 3y ≥ 0, x ≥ 0 and y ≥ 0 are (0, 0), (7, 0), (3, 4) and (0, 2), then the value of Maximum Z+3 Minimum Z is:

A91 B181 C1 D-1

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Math Chapter Wise Linear Programming Problems English KVS PGT 2023

Q67547.Which among the following is NOT a corner point of the LPP, maximize Z = 4x + y subject to the constraints, x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0?

A(0, 50) B(20, 30) C(50, 0) D(30, 0)

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Math Chapter Wise Linear Programming Problems English RPSC PGT 2022

Q67548.A necessary and sufficient condition for a basic feasible solution to a minimization linear programming problem to be an optimum is that (for all j)-

Azj – cj = 0 Bzj – cj ≤ 0 Czj – cj ≥ 0 Dzj –cj ≠ 0

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Math Chapter Wise Linear Programming Problems English RPSC PGT 2022

Q67549.Solution of minimal assignment problem whose effectiveness matrix is following – I II III IV A 2 3 4 5 B 4 5 6 7 C 7 8 9 8 D 3 5 8 4

AA → II, B → III, C → IV, D → I BA → III, B → II, C → IV, D → I CA → III, B → II, C → I, D → IV DAll above

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Math Chapter Wise Linear Programming Problems English RPSC PGT 2022

Q67550.The objective function of the dual problem of the following primal problem is – Max (z) = 3x1 – 3x2 s.t. x1≤4 x2≤6 x1+x2≤5 –x2≤–1 X1,x2≥0

AMax (Z’) = –4w1–6w2–5w3+w4 BMin (Z’) = –4w1–6w2+5w3–w4 CMin (Z’) = 4w1+6w2+5w3+w4 DMin (Z’) = 4w1–6w2–5w3+w4

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67551.In hyperplane 2x1 + 3x2 + 4x3 – x4 = 5, the point (1, 2, 3, 4) lies in -

AOpen half space of type cx > z BOpen half space of type cx < z CClosed half space of type cx ≤ z DClosed half space of type cx ≥ z

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67552.The number of basic solution to the system- 3x1 + 4x2 + 3x3 + 8x4 = 7 2x1 – 3x2 + 2x3 – 6x4 = 13

A12 B4 C9 D6

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67553.If a constraint is multiplied by a non-zero constant of a L.P.P, then the solution

ADoes not change with original solution Bis increased by addition of that non-zero constant Cis increased by multiplication of that non-zero constant Dis decreased by subtraction of that non-zero constant

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67554.For a L.P.P, Minimise z = x1 + 5x2 – 3x3, Subjected to 2x1 + x2 + x3 = 5, 3x1 – x2 + 4x3 = 5, x1, x2, x3 ≥ 0, the solution (1, 2, 1) is–

AA basic but not feasible solution BA basic feasible solution CA feasible but not basic solution DNeither basic nor feasible solution

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67555.The solution (1, 0, 1) to be system x1 + x2 + x3 = 2, x1 – 3x2 + x3 = 2, 2x1 + 3x2 + 4x3 = 6 is

AA basic feasible solution BNot a basic solution CA basic but not feasible solution DA non-degenerate basic feasible solution

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67556.The minimum cost of the assignment problem:

A52 B45 C60 D50

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67557.The optimal value of the objective function of the L.P.P, Min z = 5x1 – 2x2; subjected to 2x1 + 3x2 ≥ 1 x1, x2, ≥ 0 is–

A−4/3 B5/2 C0 D−2/3

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67558.The pay-off matrix for a strictly determinable game is– The value of b is–

A–1 ≤ b ≤ 2 B0 ≤ b ≤ 2 C–2 ≤ b ≤ 2 D–8 ≤ b ≤ 5

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Math Chapter Wise Linear Programming Problems English DSSSB PGT 2021

Q67559.Which one of the following is not a non- degenerate basic solution in a system of 2 equations with 4 unknowns?

A(10, – 42, 0, 0) B(0, 22, – 43, 0) C(0, 0, – 8, 0) D(7, 0, – 9, 0)

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Math Chapter Wise Linear Programming Problems English JSSC PGT 2018

Q67560.A solution to linear programming problem that satisfies all the constraints, except the non- negativity constraint, is referred to as:

AFeasible solution BBasic solution COptimal solution DBasic feasible solution

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