Points |
Value of z |
(0, 0) |
0 |
(0, 8) |
−32 |
(5, 0) |
15 |
(4, 10) |
−28 |
(6, 8) |
−14 |
Since for z = 3x − 4y
z(0, 0) = 3(0) − 4(0) = 0
z(0, 8) = 3(0) − 4(8) = −32
z(5, 0) = 3(5) − 4(0) = 15
z(4, 10) = 3(4) − 4(10) = − 28
z(6, 8) = 3(6) − 4(8) = 18 − 32 = −14
and z(6, 5) = 3(6) − 4(5) = 18 − 20 = −2
i.e. Z
max = 15 and Z
min = −32
∴ Maximum value of z + minimum value of z
= 15 + (−32)
= 15 − 32
i.e. Maximum value of z + minimum value of z = −17
Hence, the correct answer is option D.