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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, - Mathematics

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MCQ

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 

Options

  • p = q

  • p = 2q

  • p = 3q

  • q = 3p

     
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Solution

 q = 3p

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
Concept: Mathematical Formulation of Linear Programming Problem
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 30 Linear programming
MCQ | Q 17 | Page 68
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