Solve the following LP using the Two-Phase Method: maximize z = x 1 x 2 4 x 3 2 x 1 x 2 2 x 3 8 subject to 2 x 1 x 2 x 3 6 x 1 , x 2 , x 3 0 (a) (2 points) Modify the original LP by introducing the necessary artificial variable(s) and provide the LP formulation for Phase I. Indicate which variables are artificial. (b) (4 points) Phase I: Setup the initial tableau in canonical form, solve the LP, and determine whether the original problem is feasible or not. Justify your answer. Phase I: Tableau 0: z' Phase I: Tableau 1: z' RHS RHS Ratio 1 z' z' Ratio 1 1 Phase I: Tableau 2: RHS z' z' Ratio 1 (c) (4 points) Phase II: Setup the initial tableau in canonical form, solve the LP, and provide the optimal solution (point x and objective function value z) for the original problem. If there exist multiple optima, represent the set of all optimal solutions as a convex combination of the optimal extreme points. Phase II: Tableau 0 Phase II: Tableau 1 Phase II: Tableau 2 z z RHS RHS RHS Ratio 1 z z Ratio 1 z z Ratio 1 2