If the corners points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5) then (maximum of z- minimum of z) for the objective function $z= 4x + 6y $ is :

60

The correct answer is Option (3) → 60

$Z= 4x + 6y $

$⇒Z_{(0,2)}=4×0+6×2=12$

$⇒Z_{(3,0)}=4×3+6×0=12$

$⇒Z_{(6,0)}=4×6+6×0=24$

$⇒Z_{(0,5)}=4×0+6×5=30$

$⇒Z_{(6,8)}=4×6+6×8=72$

$∴Z_{max}-Z_{min}=72-12=60$