Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Let X1 and X2 Are Optimal Solutions of a Lpp, Then (A) X = λ X1 + (1 − λ) X2, λ ∈ R is Also an Optimal Solution (B) X = λ X1 + (1 − λ) X2, 0 ≤ λ ≤ 1 Gives an Optimal Solution - Mathematics

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MCQ

Let X1 and X2 are optimal solutions of a LPP, then

Options

  • X = λ X1 + (1 − λ) X2, λ ∈ R is also an optimal solution

  • X = λ X1 + (1 − λ) X2, 0 ≤ λ ≤ 1 gives an optimal solution

  • X = λ X1 + (1 + λ) X2, 0 ≤ λ ≤ 1 gives an optimal solution

  • X = λ X1 + (1 + λ) X2, λ ∈ R gives an optimal solution

     
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Solution

X = λ X1 + (1 − λ)X2, 0 ≤ λ ≤ 1 gives an optimal solution

A set A is convex if, for any two points, x1x2 ∈ A, and \[\lambda \in \left[ 0, 1 \right]\] imply that \[ \lambda  \text{ x } _1 + \left( 1 - \lambda \right) x_2 \in A\] .
Since, here  X1 and X2 are optimal  solutions 
Therefore, their convex combination will also be an optimal solution

Thus, X = λ X1 + (1 − λ) X2, 0 ≤ λ ≤ 1 gives an optimal solution.

Concept: Introduction of Linear Programming
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 30 Linear programming
MCQ | Q 4 | Page 67

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