5. (20p) Below is given the initial simplex tableau for a maximization type LP problem. X1, X2 and X3 are the original variables of the LP, and s and s2 are the slack variables for the first and second constraints, respectively. Z X1 X2 X3 Si S2 RHS Initial Simplex tableau Basic Row variables 0 1 S1 1 0 S2 0 Z -2 1 1 -3 1 1 -1 -1 0 0 1 0 0 0 1 0 1 2 a) Formulate the LP problem (i.e. the objective function and constraints) by looking at the initial simplex tableau. b) Find an adjacent basic feasible solution (bfs) that has a better z value than the initial bfs. c) What can you say about the solution of this LP by just inspecting the initial tableau without doing any iteration of simplex algorithm? Can this LP have an optimal solution? Can it be unbounded? Why or why not? d) Find a direction of unboundedness d for this problem by inspecting the initial tableau. Then, show mathematically that it is indeed a direction of unboundedness