CBSE Class 12 · 2023 · Linear ProgrammingMultiple Choice

The objective function

Z = a x + b y

of an LPP has maximum value 42 at

(4, 6)

and minimum value 19 at

(3, 2)

. Which of the following is true?

(A) $a = 9, b = 1$
(B) $a = 5, b = 2$
(C) $a = 3, b = 5$ ✓ Correct
(D) $a = 5, b = 3$

Answer: (C)

Solution

Substitute the given points into

Z = a x + b y

4 a + 6 b = 42 and 3 a + 2 b = 19

Multiply the second equation by 3:

9 a + 6 b = 57

.
Subtract the first equation:

5 a = 15 ⟹ a = 3

Then

3 (3) + 2 b = 19 ⟹ 2 b = 10 ⟹ b = 5

.
Hence

a = 3, b = 5

, option (C).

CBSE Class 12 Board · 2023 · Single correct option

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