If the objective function $z = px + qy$ has its maximum value at the points (2, 1) and (0, 6), then the relationship between $p$ and $q$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $2p=5q$
If the objective function $Z=px+qy$ attains its maximum value at two different corner points $(2,1)$ and $(0,6)$, then
$Z(2,1)=Z(0,6)$
$2p + q = 6q$
$2p = 5q$
$\frac{p}{q} = \frac{5}{2}$
Thus, the required relation is $2p = 5q$ or $p : q = 5 : 2$.