$7.($TA$3)($Standard and slack forms of the simplex algorithm$)$ Consider the following LP:

min x$1+$ x$2$ : $2$x$1+$ x$2>=1$

x$1+3$x$2>=1$

x$1>=0,$ x$2>=0.$

$($a$)$ Convert this into the standard form of the simplex algorithm.

$($b$)$ Convert the standard form $($derived in part $($a$))$ into the slack form.

$8.($TA$3)($Simplex algorithm$)$ Consider the following LP:

max $4$x$1+3$x$2$ : $2$x$1+3$x$2<=6$

$3$x$1+2$x$2<=3$

$2$x$2<=5$

$2$x$1+$ x$2<=4$

x$1>=0,$ x$2>=0.$

$($a$)$ Solve this using the simplex algorithm that we learned in class. You should do it by hand.

$($b$)$ Solve this using CVXPY to do sanity check for your solution in part $($a$).$