GATE Mechanical 2024 | Question: 29

Question

​​​​At the current basic feasible solution $\text{(bfs)}$ $v_{0}\left(v_{0} \in \mathbb{R}^{5}\right)$, the simplex method yields the following form of a linear programming problem in standard form.
\[
\begin{array}{ll}
\text { minimize } & z=-x_{1}-2 x_{2} \\
\text { s.t. } & x_{3}=2+2 x_{1}-x_{2} \\
& x_{4}=7+x_{1}-2 x_{2} \\
& x_{5}=3-x_{1} \\
& x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \geq 0
\end{array}
\]

Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs $v_{1}\left(v_{1} \in \mathbb{R}^{5}\right)$ that best improves the objective function, which of the following represents the objective function at $v_{1}$, assuming that the objective function is written in the same manner as above?

• A. $z=-4-5 x_{1}+2 x_{3}$
• B. $z=-3+x_{5}-2 x_{2}$
• C. $z=-4-5 x_{1}+2 x_{4}$
• D. $z=-6-5 x_{1}+2 x_{3}$