The corner points of the bounded feasible region for an LPP are (0, 4), (4, 4), (6, 6), (0, 12). If the objective function is $Z = px + qy, p > 0, q> 0$, then the condition on $p$ and $q$ so that maximum of Z occurs at (6, 6) and (0, 12) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $p = q$
Given corner points: (0, 4), (4, 4), (6, 6), (0, 12)
Objective function: $Z = px + qy$, $p>0, q>0$
Maximum occurs at (6, 6) and (0, 12) → $Z$ has same value at both points:
$p \cdot 6 + q \cdot 6 = p \cdot 0 + q \cdot 12$
$6p + 6q = 12q \Rightarrow 6p = 6q \Rightarrow p = q$
Condition on $p$ and $q$: $p = q$