$($a$)$ Select correct statements from below.

If $x^0$ is an optimal solution to the linear program LP$1$ with cost coefficient ${}_1{c}_2,$dots,$c_n$ and LP$2$ is a linear program obtained by subtracting $1$ from each of the objective functio coefficients of LP$1$ then $x^0$ will be an optimal solution to LP$2.$

If $x^0$ is an optimal solution to the linear program LP$1$ and LP$2$ is a linear program obtained by multiplying the objective function of LP $1$ by a constant $0$ then $x^0$ will be an optimal solution to LP$2.$

If $x^1$ and $x^2$ are optimal solutions to a linear program, then $=x^1+(1-)x^2,01$ is also optimal to the linear program.

$x^0=(0,0,17,1,4,0)$ is a BFS of the linear program

Maximize $3x_1+2x_2+4x_3-x_4+2x_5+x_6$

Subject $to{x}_1+x_2+x_3+2x_4-x_5+4x_6=15$

$,x_1+2x_2+x_3-x_4+x_5+5x_6=20$

$,x_{1}0,i=1,$dots,$6.$