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For each of the following linear programming models give your

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

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

(b) Maximize Z = 2x1 + 5x2 + 3x3 + 4x4 + x5,

Subject to

and

xj ≥ 0, for j = 1, 2, 3, 4, 5.

(a) Maximize Z = 10x1 - 4x2 + 7x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

(b) Maximize Z = 2x1 + 5x2 + 3x3 + 4x4 + x5,

Subject to

and

xj ≥ 0, for j = 1, 2, 3, 4, 5.

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