Hello! any help with this linear program will be appreciated

Your colleague is working on the following LP problem: Maximize z = -21 +x2 +2x3 subject to 1 + 2 02 - 23 2x1 +3x2 +23 IVIAIAIN 2x1 +4x2 +2x3 C3 He tells you that he has found an optimal solution with a dictionary where X2, 25, 26 are non-basic and X1, X3, 24 are basic. (a) 2 marks Consider the initial dictionary and the dictionary that is thought to be optimal (by your colleague). For each of these dictionaries, give the corresponding B, N, CN, CN, TB, IN, b, and remember to write in the basis headings (that is, label the columns of matrices with the corresponding variables). (b) 2 marks What is the basic solution of your colleague's (thought-to-be-optimal) dictionary? Is this a feasible solution? You have to show your work. (c) 3 marks Is your colleague's (thought-to-be-optimal) dictionary really optimal? You have to justify your