Consider the following linear programming model. max Z = 3x, + 2x, s.t. xy + 2x, 58 2x + x, 56 3x, 56 X, X, 20 a) Introduce slack variables in order to write the functional constraints in augmented form. b) Solve this problem using the simplex method geometrically by picking the origin as the starting CPF. For each iteration, you are required to provide the following information: (1) how do you do the "optimality test? (2) If not optimal, how do you choose the moving direction? (3) How far can you move? That is, specify the new CPF. You only need to perform TWO iterations at most