got a question about the simplex algorithm.
Is the optimized objective function after applying the Simplex Algorithm the optimum?
max. -4x_2 - 5x_3 -2x_4 subject to -x_1 - 2x_2 - 3x_3 <= -8 x1 - 2x_2 - 2x_3 - x_4 <= -3 x >= 0
The Simplex Algorith (In this case the Dual-Simplex Algorithm) says: Choose a row r with b_i < 0.
If I choose the first row with b_1 = -8 and pivot with min.(b_i / A_r,i) for all i € [n] = -3 the resulting objective value is after the second and last pivot step -30.
But If I choose the second row with b_2 = -3 first and pivot with -2 my resulting objective value is -11 at the end.
An online simplex tool calculated -11, too. It seems that both solutions are feasible.
I always thought that the Simplex Algorithm calculates the optimum. But -30 is not the optimum because -11 is also feasible.