OPERATIONS MANAGEMENT

Question 5 [12] Assume that the table below represents the final simplex tableau for an LP model defined in terms of non-negative decision variables #1, 12 and 13, with the objective function z that must be maximised and three functional constraints. The slack or surplus variables S1, S2 and 53, and the artificial variables a 1 and a2 were added, with si, 82, 83, 01, 02 > 0. 2 11 22 23 81 S2 83 di 02 rhs BV 0 0 P2 -1 1 4 3 -1 -3 2 11 0 1 0 0 0 2 1 0 -1 P3 02 0 0 -1 2 0 1 1 0 -1 1 S2 1 1 pi 1 1 4 3 M M - 3 6 2 In the above final simplex tableau, M represents any big number. Give conditions on parameters Pi, p2 and p3 for which the problem has the following: (a) a unique optimal solution (3) (b) multiple optimal solutions (3) (c) an unbounded solution (3) (d) no solution. (3) co