The corner points of the feasible region for an L.P.P are (0, 7), (8, 8), (9, 3) and (0, 15). If the objective function is $Z=px +qy : p, q > 0,$ then the condition on p and q so that the maximum of Z occurs at (0, 7) and (9, 3) is :

$9p=4q$

The correct answer is Option (3) → $9p=4q$

The objective function,

$Z=px +qy$

$Z(0,7)=Z(9,3)$  [Given]

$7q=9p+3q$

$4q=9p$