The corner points of the feasible region for an LPP are (0, 4), (2, 3), (4, 5), (7,0). If objective function is $Z= px+ qy ;p, q > 0$ then the condition on p and q so that the minimum of Z occurs at (2, 3) and (7,0) is :

$5p=3q$

The correct answer is Option (2) → $5p=3q$

Objective function, $Z=px+qy$

$Z_{min}=Z_{(2,3)}=Z_{(7,0)}$  [Given]

$⇒2p+3q=7p$

$⇒3q=5p$