Consider the following LPP$,$ which is being solved by the dual simplex method.

Maximize $z=-x_1+x_2$

subject $to$

$x_1-4x_{2}5$

$x_1-3x_{2}1$

$2x_1-5x_{2}1$

$x_1,x_{2}0$

Note: Answer based on the rules for entering and leaving variables of the dual simplex method.

Which of the following is true for the given problem? Select all that apply.

The optimal value of the objective function is $-5.$

The optimum solution is obtained at $x_1=5,x_2=0.$

There is no feasible solution for the given LPP$.$

The entering variable for the first iteration is $x_1.$