Problem $4$: Consider the following linear program, which does not have an immediately apparent basic feasible solution.

max$2x_1+x_2$

$-x_1,+x_{2}2$

$x_1+2x_2=8$

$-2x_1+2x_{2}6$

$x_1,x_{2}0$

Part a: Formulate a linear program that can be used to identify a basic feasible solution to the problem above. $($Hint: Read Section $4\mathrm{.}13$ of the textbook.$)$

Part b: Solve this "Phase I" linear program and specify the resulting solution. Is this a basic feasible solution to the original problem? Explain in no more than a couple sentences.