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Chapter 12 Linear Programming Ex 12.2 Solutions

Question - 11 : -
The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is
(A) p = q
(B) p = 2q
(C) p = 3q
(D) q = 3p

Answer - 11 : -

The maximum value of Z is unique

Here, it is given that the maximum value of Z occurs at twopoints, (3, 4) and (0, 5)

Value of Z at (3, 4) = Value of Z at (0, 5)

p (3) + q (4) = p (0) + q (5)

3p + 4q = 5q

3p = 5q – 4q

3p = q or q = 3p

Therefore, the correct answer is option (D)

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