The following Linear Programming problem has: Maximize: Z = x₁ + x₂ Subject…
2013
The following Linear Programming problem has:
Maximize: Z = x₁ + x₂
Subject to:
x₁ - x₂ ≥ 0
3x₁ - x₂ ≤ -3
x₁, x₂ ≥ 0
- A.
Feasible solution
- B.
No feasible solution
- C.
Unbounded solution
- D.
Single point as solution
Attempted by 11 students.
Show answer & explanation
Correct answer: B
Correct answer: No feasible solution
The constraints contradict the non-negativity condition.
From x₁ - x₂ ≥ 0, we get x₁ ≥ x₂.
From 3x₁ - x₂ ≤ -3, we get x₂ ≥ 3x₁ + 3.
Combining the two gives x₁ ≥ x₂ ≥ 3x₁ + 3, so x₁ ≥ 3x₁ + 3.
This simplifies to -2x₁ ≥ 3, or x₁ ≤ -1.5.
But the problem also requires x₁ ≥ 0, which is impossible together with x₁ ≤ -1.5.
Therefore: the feasible region is empty, so the linear program has no feasible solution.
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