(Solved): Exercise 5 (two-phase method). Solve the following linear programming problem using the two-phase s ...

Exercise 5 (two-phase method). Solve the following linear programming problem using the two-phase simplex method \\[ \\text { maximize } x_{1}+x_{2}+x_{3} \\] subject to \\[ \\begin{array}{l} x_{1}+3 x_{2}+x_{3}=3 \\\\ x_{1}-2 x_{2}-2 x_{3}=4 \\\\ x_{1}, x_{2}, x_{3} \\geq 0 \\end{array} \\] 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.