(Solved): Exercise 6 (two-phase method). Solve the following linear programming problem using the two-phase s ...

Exercise 6 (two-phase method). Solve the following linear programming problem using the two-phase simplex method \\[ \\operatorname{minimize} \\quad x_{1}+x_{2}+x_{3} \\] subject to \\[ \\begin{array}{l} x_{1}-x_{2}+x_{3} \\geq 3 \\\\ x_{1}+2 x_{2}+7 x_{3} \\leq 4 \\\\ x_{1}, x_{2}, x_{3} \\geq 0 \\end{array} \\] Start by adding slack variables and note that the problem was to minimize rather than maximize. 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.