Mathematics · Linear Programming
A Primal Linear Programming Problem is given as: Maximize Z = 5x1 + 12x2 + 4x3 subject to the constraints x1 + 2x2 + x3 ≤ 10, 2x1 - x2 + 3x3 = 8, and x1, x2, x3 ≥ 0. Determine the correct formulation of its corresponding Dual problem.
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- 1Minimize W = 10y1 + 8y2 subject to y1 + 2y2 ≥ 5, 2y1 - y2 ≥ 12, y1 + 3y2 ≥ 4, with y1 unrestricted and y2 ≥ 0.
- 2Minimize W = 5y1 + 12y2 + 4y3 subject to y1 + 2y2 + y3 ≥ 10, 2y1 - y2 + 3y3 = 8, with y1, y2, y3 ≥ 0.
- 3Minimize W = 10y1 + 8y2 subject to y1 + 2y2 ≤ 5, 2y1 - y2 ≤ 12, y1 + 3y2 ≤ 4, with y1 ≥ 0 and y2 ≥ 0.
- 4Minimize W = 10y1 + 8y2 subject to y1 + 2y2 ≥ 5, 2y1 - y2 ≥ 12, y1 + 3y2 ≥ 4, with y1 ≥ 0 and y2 unrestricted.✓
Correct answer
Minimize W = 10y1 + 8y2 subject to y1 + 2y2 ≥ 5, 2y1 - y2 ≥ 12, y1 + 3y2 ≥ 4, with y1 ≥ 0 and y2 unrestricted.
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