Question

The feasible region of a LPP is shown in the given figure. Let x = 3x – 4y be the objective function. Minimum of z occurs at



(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)

Answer 1

Points	Value of z
(0, 0)	0
(0, 8)	−32
(5, 0)	15
(4, 10)	−28
(6, 8)	−14

For z = 3x − 4y
z(0, 0) = 3(0) − 4(0)
i.e. z(0, 0) = 0
z(0, 8) = 3(0) − 4(8)
= 0 − 32
z(0, 8) = −32
z(5, 0) = 3(5) − 4(0)
z(5, 0) = 15
z(4, 10) = 3(4) − 4(10)
= 12 − 40
i.e. z(4, 10) = −28
z(6, 8) = 3(6) − 4(8)
= 18 − 32
i.e. z(6, 8) = −14
and z(6, 5) = 3(6) − 4(5) = 18 − 20 = −2
∴ Minimum of z occurs at (0, 8) i.e. Z_min = −32
Hence, the correct answer is option B.