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Required information

Consider the following problem.

Maximize $Z=-x_1+4x_2,$

subject to

$-3x_1+x_{2}6$

$x_1+2x_{2}4$

and

$x_2-3,($no lower bound constraint for $x_1)$

Reformulating the given problem, as shown below, demonstrates that it has only two functional constraints and all variables have non$-$negativity constraints. Identify if the given model is true or false.

Maximize $Z=-x_1^{+}+x_1^{-}+4x_3-12$

subject to

$-3x_1^{+}+3x_1^{-}+x_{3}9$

$x_1^{+}-x_1^{-}+2x_{3}10$

and

$x_1^{+}0,x_1^{-}0,x_{3}0.$