2. (20 points) Consider the following dictionary, obtained during some intermediate iteration of phase I of the simplex method. The variables 13, 14, and I5 are slack variables and ro is the artificial variable added in the auxiliary LP. Carry out one iteration of the simplex method using Dantzig's rule for variable selection (choose the smallest subscript to break ties). Answer the following questions: (a) How did you choose the entering variable? (b) How did you choose the leaving variable? (c) Carry out the pivot operation and obtain the next dictionary. Show your steps. (d) Is the new dictionary you obtained optimal for Phase I? Explain. (e) From the dictionary you obtained, what (if any) can you conclude about the original LP associated with the auxiliary LP being solved in Phase I? -3 + 2.11 + .22 3.23 24 3 22 + 13 2 + 2.62 + 13 25 8 2:01 2.x2 + 13 11 10 1 2. (20 points) Consider the following dictionary, obtained during some intermediate iteration of phase I of the simplex method. The variables 13, 14, and I5 are slack variables and ro is the artificial variable added in the auxiliary LP. Carry out one iteration of the simplex method using Dantzig's rule for variable selection (choose the smallest subscript to break ties). Answer the following questions: (a) How did you choose the entering variable? (b) How did you choose the leaving variable? (c) Carry out the pivot operation and obtain the next dictionary. Show your steps. (d) Is the new dictionary you obtained optimal for Phase I? Explain. (e) From the dictionary you obtained, what (if any) can you conclude about the original LP associated with the auxiliary LP being solved in Phase I? -3 + 2.11 + .22 3.23 24 3 22 + 13 2 + 2.62 + 13 25 8 2:01 2.x2 + 13 11 10 1