Use the dual simplex method to solve: Maximize z = −2x₁ − 3x₂ subject to x₁ + x₂ ≥ 2, 2x₁ + x₂ ≤ 10, x₁ + x₂ ≤ 8, x₁, x₂ ≥ 0.

1. Ax₁ = 2, x₂ = 0 and z = −4
2. Bx₁ = 2, x₂ = 6 and z = −22
3. Cx₁ = 0, x₂ = 2 and z = −6
4. Dx₁ = 6, x₂ = 2 and z = −18

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. x₁ = 2, x₂ = 0 and z = −4

Explanation

Maximizing −2x₁ − 3x₂ means making 2x₁ + 3x₂ as small as possible while x₁ + x₂ ≥ 2. x₁ is cheaper, so x₁ = 2, x₂ = 0 (which satisfies the other constraints), giving z = −4.