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:

$2p=5q$

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 $p : q = 5 : 2$.