GATE 2024 Mechanical Engineering Q39

Question

At the current basic feasible solution (bfs) $\boldsymbol{v_0}$ ($\boldsymbol{v_0} \in \mathbb{R}^5$), the simplex method yields the following form of a linear programming problem in standard form.
minimize $z = -x_1 - 2x_2$
s. t.
$x_3 = 2 + 2x_1 - x_2$
$x_4 = 7 + x_1 - 2x_2$
$x_5 = 3 - x_1$
$x_1, x_2, x_3, x_4, x_5 \ge 0$
Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs $\boldsymbol{v_1}$ ($\boldsymbol{v_1} \in \mathbb{R}^5$) that best improves the objective function, which of the following represents the objective function at $\boldsymbol{v_1}$, assuming that the objective function is written in the same manner as above?

Answer

$z = -4 - 5x_1 + 2x_3$

Answer

$z = -3 + x_5 - 2x_2$

Answer

$z = -4 - 5x_1 + 2x_4$

Answer

$z = -6 - 5x_1 + 2x_3$