(Solution) - Solve the dual of the following problem then find its -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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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