For the following LP$,$ identify three alternative optimal basic solutions, and then write a general expression for all the nonbasic alternative optima comprising these three basis solutions:

maximize $z=x_1+2x_2+3x_3$

subject $to{x}_1+2x_2+3x_{3}10$

$,x_1+x_{2}5$

$,x_{1}1$

$,x_1,x_2,x_{3}0$

Note: Although the problem has more than three alternative basic solution optima, you are only required to identify three of them.