The corner points of the feasible region associated with the LPP: Maximise \(Z = px + qy,\ p, q \gt 0\) subject to \(2x + y \le 10,\ x + 3y \le 15,\ x, y \ge 0\) are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(q = 3p\)
If the optimum occurs at two corner points, Z has the same value at both points:
\(Z(3, 4) = Z(0, 5)\)
\(3p + 4q = 5q\)
\(q = 3p\)