The corner points of the feasible region determined by the following system of linear

Monjur Alahi

The corner points of the feasible region determined by the following system of linear inequalities: 2x+y≤10,x+3y≤15,xy≥ 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


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Salim Ahmed Kawsar

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The maximum value of Z is unique.
It is given that the maximum value of Z occurs at two points, (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
⇒ q = 3p
Hence, the correct answer is D.

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