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The corner points of the bounded feasible region determined by a system of linear constraints are (0,3),(1,1) and (3,0). Let Z = px + qy , where p,q>0. The condition on p and q so that the minimum of Z occurs at ( 3,0 ) and ( 1,1 ) is

(a) p=2q              (b) p=q/2                   (c) p=3q                     (d) p=q

This question is similar to Question 38 Choice-2 CBSE Class 12 Sample Paper for 2021 Boards



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The corner points given are (0, 3) ,(1, 1) and (3, 0) Since, minimum Z occurs at (3, 0) and (1,1) Thus Value of 𝑍=𝑝𝑥+𝑞𝑦 at (3, 0) = Value of 𝑍=𝑝𝑥+𝑞𝑦 at (1, 1) p(3) + q(0) = p(1) + q(1) 3p = p + q 3p − p = q 2p = q p = 𝒒/𝟐 So, the correct answer is (b)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.