Consider the following linear programming problem: minimize the cost 3x1+x2+ 9x3+x4 subject to xi≥0 and x1+ 2x3+x4≥4 x2+x3−x4≥2 Write out the dual problem and sketch the feasible region. Solve the dual problem by first identifying the corners of the feasible region. Which of inequalities in the dual problem are strict inequalities at the optimal point?(Note that the corresponding xi would need to be zero in order to satisfy the complementaryslackness condition (c−yA)x= 0.) Use the hint above to solve the primal problem.

Consider the following linear programming problem: minimize the cost 3x1+x2+ 9x3+x4 subject to xi≥0 and

x1+ 2x3+x4≥4

x2+x3−x4≥2

Write out the dual problem and sketch the feasible region. Solve the dual problem by first identifying the corners of the feasible region. Which of inequalities in the dual problem are strict inequalities at the optimal point?(Note that the corresponding xi would need to be zero in order to satisfy the complementaryslackness condition (c−yA)x= 0.) Use the hint above to solve the primal problem.