Maximize Z $=9$X$1+12$X$2$

subject to

X$1+$ X$210$

X$1+2$X$212$

X$1,$ X$2^30$

Solve the above LP problem by the simplex method. Provide the values of the basic variables $($BV$)$ at the second tableau and the optimal solution of the LP$.$

Select one:

BV: s$1=0,$ s$2=12|$ Optimal sol: X$1=8,$ X$2=0,$ Z $=72$

BV: s$1=4,$ x$2=6|$ Optimal sol: X$1=8,$ X$2=2,$ Z $=96$

BV: s$1=10,$ s$2=12|$ Optimal sol: X$1=8,$ X$2=0,$ Z $=72$

BV: s$2=0,$ x$2=0|$ Optimal sol: X$1=8,$ X$2=2,$ Z $=96$

None of the options provided