Answer: write this as a new Lp! Add to each equation one artificial variable Objective: Minimize the sum of the artificial variables. Multiply by -l if necessary to find positive b Minimize z xn+1+…+xn+m Subject to aux,+.+a,x, +ru, amIx +x=b x1≥0,,xn≥0,xn+1≥0.x+m≥0. Phase i of simplex algorithm The new LP on the previous slide is phase I of the general simplex algorithm. Note that an inconsistent system of equations will be revealed as such by a positive Phase I optimum. Thus, LP can function as a check for consistency of linear systems of equations Phase Ii uses as a starting basis the feasible corner point solution found in Phase IAnswer: write this as a new LP! • artificial variable. Objective: Minimize the sum of the artificial variables. bi , 0 0. ... Subject to ... Minimize ... 1 1 1 1 11 1 1 1 1 1 t t t t               n n n m m mn n n m m n n n n n m x x x x a x a x x b a x a x x b Z x x      Phase I of simplex algorithm • general simplex algorithm. Note that an inconsistent system of equations will be revealed as such by a positive Phase I optimum. Thus, LP can function as a check for consistency of linear systems of equations. • point solution found in Phase I. Add to each equation one – Multiply by –1 if necessary to find positive 0, 0, The new LP on the previous slide is phase I of the Phase II uses as a starting basis the feasible corner