I've been asked to solve this problem using the Dual Simplex Method. $$ \begin{array}{ll} \min: & x_1+6x_2+3x_3 \\ \text{s.t}: & -4x_1-4x_2-2x_3+x_4=-18 \\ & 2x_1+2x_2-4x_3+x_5 = -16 \\ & x_j \geq 0, \; j=1,\dots,5 \end{array} $$ Once I solved it, I got the Optimal Primal Solution is $x_1=2, \, x_3=5, \, x_2=x_4=x_5=0 \; \text{and} \; z = 17.$
Now I want to find the Optimal Dual Solution without solving de Dual Problem (just knowing the Optimal Primal Solution). But I don't know how to proceed.