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  x2  2x3 40 x1  x2  x3 90 2x1  x2  x3 20 and x1  0, x2  0, x3  0.

(b) Maximize Z 2x1  5x2  3x3  4x4  x5, subject to x1  3x2  2x3  3x4  x5 6 4x1  6x2  5x3  7x4  x5 15 and xj  0, for j 1, 2, 3, 4, 5.