Maximize Z $=0\mathrm{.}08$X$1+0\mathrm{.}09$X$2$

Subject to

X$1>=$ $$125,000$

X$2<=$ $$100,000$

X$1+$ X$2=$ $$250,000$

X$1,$ X$2>=0$

Solve the above problem with the simplex method. Provide the value of the basic variables $($BV$)$ at tableau #$3$ and the optimal solution of the LP$.$

Notes:

Set M $=100.$

Tableau #$1$ is the initial tableau where an inconsistency exists on row z$.$

Tableau #$2$ is the tableau where the inconsistency on row z is fixed.

Set s$2$ as the slack variable for constraint $2.$

The answers below use $$K$$ to represent $1,000$ units.

Select one:

BV: X$1=125$K$,$ X$2=100$K$,$ s$1=125$K $|$ Optimal sol: X$1=250$K$,$ X$2=100$K$,$ Z $=29$K

BV: A$1=125$K$,$ s$2=100$K$,$ A$2=250$K $|$ Optimal sol: X$1=150$K$,$ X$2=100$K$,$ Z $=21$K

None of the options provided

BV: A$1=125$K$,$ s$2=100$K$,$ A$2=250$K $|$ Optimal sol: X$1=200$K$,$ X$2=100$K$,$ Z $=25$K

BV: X$1=125$K$,$ s$2=100$K$,$ A$2=125$K $|$ Optimal sol: X$1=150$K$,$ X$2=100$K$,$ Z $=21$K