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

Last updated at Nov. 19, 2021 by Teachoo

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

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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