For the LPP: maximize Z = 2x₁ − x₂ + 2x₃ subject to 2x₁ + x₂ ≤ 10, x₁ + 2x₂ − 2x₃ ≤ 20, x₁ + 2x₃ ≤ 5, x₁, x₂, x₃ ≥ 0, what is the solution after the first simplex iteration?

1. Ax₁ = 5/2, x₂ = 0, x₃ = 0, Z = 5
2. Bx₁ = 0, x₂ = 0, x₃ = 5/2, Z = 5
3. Cx₁ = 0, x₂ = 5/2, x₃ = 0, Z = −5
4. Dx₁ = 0, x₂ = 0, x₃ = 10, Z = 20

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Show answer & explanation

Correct answer: B. x₁ = 0, x₂ = 0, x₃ = 5/2, Z = 5

Explanation

x₁ and x₃ tie for the largest coefficient (2). Bringing in x₃, the only limiting row is x₁ + 2x₃ ≤ 5, so x₃ = 5/2 and Z = 5 (the official key's choice of entering variable).