The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (2, 4), (7, 3) and (5, 0). If the maximum value of z = px + qy, where p, q > 0 occurs at both (2, 4) and (7, 3), then:

5p = q

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

Maximum occurs at $(2,4),(7,3)$

$⇒Z(2,4)=Z(7,3)$

$⇒2p+4q=7p+3q⇒q=5p$