The corner points of a bounded feasible region are (0, 5), (6, 1), (17, 2) and (4, 29). If the maximum value of objective function $z = px + qy$ where $p$ and $q >0$ occurs at two points (17, 2) and (4, 29), then the relation between $p$ and $q$ is:

$13p = 27q$

The correct answer is Option (2) → $13p = 27q$

$z=px+qy$ attains the same value at $(17,2)$ and $(4,29)$.

$17p+2q=4p+29q$

$13p=27q \;\Rightarrow\; \frac{p}{q}=\frac{27}{13}$

Relation: $13p=27q$ (i.e., $\frac{p}{q}=\frac{27}{13}$).