For an objective function ๐‘ = ๐‘Ž๐‘ฅ + ๐‘๐‘ฆ, where ๐‘Ž, 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‘ − 3๐‘Ž = 0  (b) ๐‘Ž = 3๐‘

(c) ๐‘Ž + 2๐‘ = 0  (d) 2๐‘Ž − ๐‘ = 0

 

This question is inspired from Ex 12.2, 11 (MCQ) - Chapter 12 Class 12 - Linear Programming

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Question 41 For an objective function ๐‘ = ๐‘Ž๐‘ฅ + ๐‘๐‘ฆ, where ๐‘Ž, 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‘ โˆ’ 3๐‘Ž = 0 (b) ๐‘Ž = 3๐‘ (c) ๐‘Ž + 2๐‘ = 0 (d) 2๐‘Ž โˆ’ 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 โˆ’ 30b 30a = 10b Dividing by 10 both sides 3a = b 0 = b โˆ’ 3a b โˆ’ 3a = 0 So, the correct answer is (A)

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Davneet Singh
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.