please provide with detailed solution. Thanks

1. The following is an intermediate dictionary of the Auxiliary Problem of an LP: TO -21 -22 23 -2.31 3 2 7 -3 +34 +34 -2.x2 +24 +22 -14 25 -321 +31 W = (a) How many decision variables were there in the original LP? Why? (b) Carefully perform a pivot on this dictionary choosing X2 to enter the basis and write down the new dictionary you obtain. (c) Based on (b), is the original LP feasible? If yes, write down a basic feasible solution of the original LP. (d) Is it possible for the Auxiliary Problem of an LP (in Phase I) to be unbounded? Give reasons for your