Shaded region in the figure shows the feasible solutions for a LPP. If the objective function $Z=ax+6y$ attains the maximum value at both the points (4, 10) and (6, 9) then the maximum value of Z is :

72

The correct answer is Option (4) → 72

The objective function is,

$Z=ax+6y$

$Z(4,10)=Z(6,9)$

$4a+60=6a+54$

$2a=6$

$a=3$

$⇒Z(4,10)=4×3+60=72$