Question

Corner points of the feasible region for an LPP are : (0, 2), (3,0), (6,0), (6, 8) and (0, 5). Let z = 4x + 6y be the objective function. Then, Max. $z-\mathrm{Min}z=$
(a) 60
(b) 48
(c) 42
(d) 18

Answer 1

Points	Value of z
(0, 2)	12
(3, 0)	12
(6, 0)	24
(6, 8)	72
(0, 5)	30

For 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(6, 8) = 4(6) + 6(8) = 72
z(0, 5) = 4(0) + 6(5) = 30
∴ Z_max = 72 and Z_min = 12
∴ Zmax − Zmin = 72 − 12 = 60
Hence, the correct answer is option A.