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GATE ME 2024 Set 1 — Question 39

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MCQ+2 / -0.67HardLP (Graphical & Simplex)Operations ResearchIndustrial Engineering

Industrial Engineering → Operations Research → LP (Graphical & Simplex)

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Question

At the current basic feasible solution (bfs) v0\mathbf{v}_0 (v0∈R5\mathbf{v}_0 \in \mathbb{R}^5), the simplex method yields the following form of a linear programming problem in standard form.minimize z=−x1−2x2\text{minimize } z = -x_1 - 2x_2s. t. x3=2+2x1−x2\text{s. t. } x_3 = 2 + 2x_1 - x_2x4=7+x1−2x2x_4 = 7 + x_1 - 2x_2x5=3−x1x_5 = 3 - x_1x1,x2,x3,x4,x5≥0x_1, x_2, x_3, x_4, x_5 \geq 0Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs v1\mathbf{v}_1 (v1∈R5\mathbf{v}_1 \in \mathbb{R}^5) that best improves the objective function, which of the following represents the objective function at v1\mathbf{v}_1, assuming that the objective function is written in the same manner as above?
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