Question 1 - NCERT Exemplar - MCQs - Chapter 12 Class 12 Linear Programming (Term 1)

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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)