Question

3. (2 points) The tableau r421 21 02 5 3 2 10 1 6 4 2 1 0 0 0 represents a solution to the linear programming problem Minimize z 41 22 + r3, subject to the constraints 31 +2a2+r3 6, that satisfies the optimality criterion but is infeasible. Use the dual simplex method to restore feasiblity and hence find an optimal solution.

Answer 1

Solution:

Given that

Maximize z = -4x_1 - 2x_2 - x_3 s.t -2x_1 - x_2 - 2x_3 lessthanorequalto -2 3x_1 + 2x_2 + x_3 lessthanorequalto 6 x_1, x_2, x_3 greaterthanorequalto 0. Standard form: Maximize z = -4x_1 - 2x_2 - x_3 + (0)x_4 + (0)x_5 s.t -2x_1 - x_2 - 2x_3 + x_4 = -2 3x_1 + 2x_2 + x_3 + x_5 = 6 x_i lessthanorequalto 0, i = 1(1)5 \r\n Since z_j - c_j greaterthanorequalto 0 Forall j = 1(1)5 and b_j greaterthanorequalto 0 Forall j (b_j = (1, 5)) So the solution is feasible and thus optimalilty is reached so, x_1 = 0, x_2 = 0, x_3 = 1. Therefore Z_min = 4 times 0 + 2 times 0 + 1 Z_min = 1