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Solve the dual of the following problem, then find its optimal solution from the solution of the dual. Does the solution of the dual offer computational advantages over solving the primal directly?

Minimize z = 5x1 + 6x2 + 3x3

Subject to

5x1 + 5x2 + 3x3 ≥ 50

X1 + x2 - x3 ≥ 20

7x1 + 6x2 - 9x3 ≥ 30

5x1 + 5x2 + 5x3 ≥ 35

2x2 + 4x2 - 15x3 ≥ 10

12x1 + 10x2 ≥ 90

X2 - 10x3 ≥ 20

X1, x2, x3 ≥ 0

Minimize z = 5x1 + 6x2 + 3x3

Subject to

5x1 + 5x2 + 3x3 ≥ 50

X1 + x2 - x3 ≥ 20

7x1 + 6x2 - 9x3 ≥ 30

5x1 + 5x2 + 5x3 ≥ 35

2x2 + 4x2 - 15x3 ≥ 10

12x1 + 10x2 ≥ 90

X2 - 10x3 ≥ 20

X1, x2, x3 ≥ 0

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