At the current basic feasible solution (bfs) $v_0 (v_0 \in \mathbb{R}^5)$, the simplex method yields the following form of a linear programming problem in standard form:
minimize $z = -x_1 - 2x_2$
s.t.
$x_3 = 2 + 2x_1 - x_2$
$x_4 = 7 + x_1 - 2x_2$
$x_5 = 3 - x_1$
$x_1, x_2, x_3, x_4, x_5 \geq 0$
Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs $v_1 (v_1 \in \mathbb{R}^5)$ 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?
Subject to $$\,\,\,\,\,\,\,\,\,\,{x_1} + 2{x_2} \le 10,$$
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1} - {x_2} \le 8, \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x_1},{x_2} \ge 0 \cr} $$
In the starting simplex tableau, $${x_1}$$ and $${x_2}$$ are non-basic variables and the value of $$Z$$ is zero. The value of $$Z$$ in the next simplex tableau is __________________.
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