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The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20).Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

(A)p = q                   (B) p = 2q

(C) q = 2p               (D) q = 3p

This question is similar to Ex 12.2, 11 - Chapter 12 Class 12 - Linear Programming

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Question 1 The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20).Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is p = q (B) p = 2q (C) q = 2p (D) q = 3p Given corner points are (0, 10), (5, 5), (15, 15), (0, 20) Max. Z = px + qy Since maximum value of Z occurs on (15, 15) and (0, 20) Hence, Value on (15, 15) = Value on (0, 20) 15p + 15q = 20q 15p = 20q − 15q 15p = 5q 15𝑝/5 = q 3p = q q = 3p ∴ Value of Z will be maximum if q = 3p So, the correct answer is (D)

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.