Problem 1: For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize Z= 10x1 -4x2 + 7x3, subject to 3x1 - X2 + 2x3 $ 25 X1 - 2x2 + 3x3 $ 25 5x1 + 2 + 2x3 5 40 *+ X2+ X3 90 2x1 - *2 + X3 20 and x1 20. X2 20, X3 2 0. (b) Maximize Z = 2x1 + 5x2 + 3x3 + 4x4 + x5, subject to X1 + 3x2 + 2x3 + 3x4 + X5 = 6 4x, + 612 + 5X3 + 7x4 + X's $ 15 and x, 20, for j = 1, 2, 3, 4, 5