$1.$ Consider the LP: Maximize z $=$ x $+2$y

Subject to

$4$x $+$ y $<=4$

x $+$ y $>=1$

$3$x $+$ y $<=0$

x$,$ y $>=0$

In both steps below, don$$t forget to encode the correct objective in the initial tableau, and make sure that objective row in the initial tableau two satisfies tableau properties $($ie$,$ all basic variable cols are zero$).$

$($a$)$ Since the non$-$negative slack variable in the second constraint cannot act as a basic variable, add an artificial variable to that constraint. Now, solve phase one, where the objective is to minimize the sum of artificial variables.

$($b$)$ From the final tableau of phase $1,$ is the original LP feasible or infeasible? If it is feasible, do phase two.