Question 5 (50%). Consider the following problem. = + 3x3 Minimize Z = subject to 2x1 + X2 5x1 + 2x2 + 7X3 = 420 3x1 + 2x2 + 5x3 > 280 Xi > 0, x2 > 0, X3 > 0. (1) (2) (a) Reformulate the problem so that the goal is maximizing an objective function, the right-hand-side of each functional constraint is non-negative and each variable has a non-negativity constraint. (b) Construct the phase-1 problem in algebraic/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. (c) Work through the phase-1 of the two-phase method in tabular form to find a feasible solution for (x1, X2, 23) to the problem. In each simplex tableau, identify the current solution for (21, 22, 23) and state its feasibility in the original problem. (d) Construct the phase-2 problem in algebraic/tabular form. Then, work through the phase-2 of the two-phase method in tabular form to determine ALL optimal solutions for (x1, 22, 23) and the associated optimal value for Z. In each simplex tableau, identify the current solution for (21, 22, 23) and the associated value for Z. 2