# Question

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.

## Answer to relevant Questions

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