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Questions › IIT JAM › IIT JAM 2023 › Q19
2 marks, −0.667Mathematics › Constrained optimisation and linear programming › Linear programming dualityHardabout 3 min

IIT JAM 2023 Question 19: Constrained optimisation and linear programming

For the LP (P)(P)(P): minimise z=4x1+6x2+6x3z=4x_1+6x_2+6x_3z=4x1​+6x2​+6x3​ subject to x1+3x2≥3x_1+3x_2\ge3x1​+3x2​≥3, x1+2x3≥5x_1+2x_3\ge5x1​+2x3​≥5, x≥0x\ge0x≥0. If x∗x^*x∗ is optimal, z∗z^*z∗ the optimal value, and w∗=(w1∗,w2∗)w^*=(w_1^*,w_2^*)w∗=(w1∗​,w2∗​) the dual optimum, then

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For the LP (P): minimise z=4x₁+6x₂+6x₃ subject to x₁+3x₂≥3, x₁+2x₃≥5, x≥0. If x* is optimal, z* the optimal value, and w*=(w₁*,w₂*) the dual optimum, then (A) x₂*+x₃*=w₁*+w₂* (B) z*=4(x₁*+w₂*) (C) z*=6(w₁*+x₃*) (D) x₁*+x₃*=w₁*+w₂*

Also written as: For the LP (P): minimise z=4x_1+6x_2+6x_3 subject to x_1+3x_2>=3, x_1+2x_3>=5, x>=0. If x* is optimal, z* the optimal value, and w*=(w_1*,w_2*) the dual optimum, then

Constrained optimisation and linear programming has come up 44 times in 7 exams since 2007.

What this question tests

This question is on Linear programming duality, part of Constrained optimisation and linear programming in Mathematics.

Pairing a linear program with its dual and what their solutions say about each other.

TestStop has 7 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2022 · Q22An initial simplex tableau has Cⱼ row 15, 25, 0, -M, -M, 0 over columns x, y, S₁, A₁, A₂, S₃, with basis A₁…
  • IIT JAM 2021 · Q22(x₁* = 1, x₂* = 0, x₃* = 2) is optimal for: minimize x₁ + 5x₂ + 2x₃ subject to x₁ - x₂ ≤ 1, x₁ + x₂ + x₃ ≥…
Take this paper as a timed mockMore on Linear programming duality

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