$3-14.$ Consider the following LP:

Maximize $z=2x_1+3x_2+5x_3$

subject to

$-6x_1+7x_2-9x_{3}4$

$x_1+x_2+4x_3=10$

$x_1,x_{3}0$

$x_2$ unrestricted

Conversion to the equation form involves using the substitution $x_2=x_2^{-}-x_2^{+}.$ Show that

a basic solution cannot include both $x_2^{-}$and $x_2^{+}$simultaneously.