Which of the following cannot be a constraint of a linear programming problem in the variables x and y?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(xy \le 12\)
The constraints of a linear programming problem are linear inequalities or equations: each side has only terms like ax, by and constants.
The product xy is a term of degree 2, so \(xy \le 12\) is not linear and cannot be a constraint.
Why the other options are incorrect
Option (1) \(2x - 3y \le 6\) — Incorrect. It is linear in x and y.
Option (2) \(\displaystyle\frac{x}{2} + \frac{y}{3} \ge 1\) — Incorrect. The coefficients are fractions, but it is still linear: \(3x + 2y \ge 6\).
Option (3) \(x \le 4y\) — Incorrect. It is linear: \(x - 4y \le 0\).