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Question

In Q. No. 24, (Maximum Value of z + Minimum Value of z) is equal to
(a) 13
(b) 1
(c) –13
(d) –17

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Solution

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. Zmax = 15 and Zmin = −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.

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