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 3x - x2 + 2xz < 25 X1 - 2x2 + 3x3 = 25 5x + x2 + 2x3 = 40 x1 + x2 + x3 = 90 2x1 - x2 + x3 = 20 and x, 20, 20, x2 > 0. (b) Maximize Z = 2xy + 5x2 + 3x3 + 4X4 + X5, subject to x1 + 3x2 + 2x3 + 3x4 + x3 = 6 4x1 + 6x2 + 5xz + 7x4 + x3 = 15 and x; 20, for j = 1, 2, 3, 4, 5.