Exercise $5($two$-$phase method$).$ Solve the following linear programming problem

using the two$-$phase simplex method

maximize x$1+$x$2+$x$3$

subject to

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

x$12$x$22$x$3=4$

x$1$ x$2$ x$30$

In Phase $1,$ set up an auxiliary LP problem that either proves the original problem

is infeasible or provides a basic feasible solution to the original problem. If Phase

$1$ yields a basic feasible solution, then proceed to Phase $2$ solve the original LP

problem starting from this basic feasible solution