The following LPP: Maximize z = 100x₁ + 2x₂ + 5x₃ subject to 14x₁ + x₂ − 6x₃ + 3x₄ = 7, 32x₁ + x₂ − 12x₃ ≤ 10, 3x₁ − x₂ − x₃ ≤ 0, x₁, x₂, x₃, x₄ ≥ 0, has

1. ASolution: x₁ = 100, x₂ = 0, x₃ = 0
2. BUnbounded solution
3. CNo solution
4. DSolution: x₁ = 50, x₂ = 70, x₃ = 60

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

Show answer & explanation

Correct answer: B. Unbounded solution

Explanation

Take x₁ = 0, x₂ = x₃ = t and x₄ = (7 + 5t)/3. All constraints hold for every t ≥ 0 (−11t ≤ 10, −2t ≤ 0), and z = 7t grows without limit.