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 the objective function. The minimum value of z occurs at
(a) (0, 2) only
(b) (3, 0) only
(c) the mid-point of the line segment joining the points (0, 2) and (3, 0) only
(d) any point on the line segment joining the points (0, 2) and (3, 0)

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)
z(0, 2) = 12
z(3, 0) = 4(3) + 6(0)
z(3, 0) = 12
and z(6, 0) = 4(6) + 6(0)
z(6, 0) = 24
z(6, 8) = 4(6) + 6(8)
= 24 + 48
z(6, 8) = 72
and z(0, 5) = 4(0) + 6(5)
i.e. z(0, 5) = 30
∴ min z occur at (0, 2) and (3, 0)
∴ minimum value of Z occur at any point on the line segment (0, 2) and (3,0)
∴ Hence, the correct answer is option D.