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Transform the following linear programming model into proper form for solution by the simplex method (including the artificial variable) and generate the initial simplex tableau. Determine the entering variable and leaving variable.
Minimize Z = 40x1 + 55x2 + 30x3
Subject to
x1 + 2x2 + 3x3 ≤ 60
2x1 + x2 + x3 = 40
x1 + 3x2 + x3≥50
5x2 + 3x3≥100
x1,x2,x3 ≥ 0

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