CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Question 41 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Sept. 8, 2021 by Teachoo

For an objective function ๐ = ๐๐ฅ + ๐๐ฆ, where ๐, ๐ > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:

Question 41 For an objective function ๐ = ๐๐ฅ + ๐๐ฆ, where ๐, ๐ > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is: (a) ๐ โ 3๐ = 0 (b) ๐ = 3๐ (c) ๐ + 2๐ = 0 (d) 2๐ โ ๐ = 0
Since maximum Z occurs at both the points (30, 30) and (0, 40)
Value of Z at both these points will be same
Therefore
30a + 30b = 40b
30a = 40b โ 30b
30a = 10b
Dividing by 10 both sides
3a = b
0 = b โ 3a
b โ 3a = 0
So, the correct answer is (A)

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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.