I have been given an LPP problem and asked to prove the basic solution $(x_1, x_2)$ is not optimal, but every time I am solving it using simplex and the duality method the objective function keeps coming same ($\max z = \min w$). What am I missing here?
The original model/problem:
$$\max z = 2x_1 + 4x_2 + 4x_3 - 3x_4$$ $$\text{Subject to: }\qquad\qquad\qquad\qquad\qquad\qquad$$ $$x_1 + x_2 + x_3 ≤ 4$$ $$x_1 + 4x_2 + x_4 = 8$$ $$x_1, x_2, x_3, x_4 ≥ 0$$
Use the dual problem to verify the basic solution $x_1, x_2$ is not optimal.