The corner points of the bounded feasible region determined by the system of linear constraints are (0, 0), (5, 0), (3, 4) and (0, 5). Let \(Z= px + qy\) where \(p, q \gt 0\). Condition on \(p\) and \(q\) so that the maximum of Z occurs at both (5, 0) and (3, 4) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2q=p\)
If the maximum occurs at both points, Z must take the same value at both corners:
\(Z(5, 0) = Z(3, 4)\)
\(5p = 3p + 4q\)
\(2p = 4q\)
\(p = 2q\)
With p = 2q this common value 10q is indeed the maximum: the other corners give \(Z(0, 0) = 0\) and \(Z(0, 5) = 5q\), both smaller.