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  • Please solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 4 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 4 maths textbook solution.

Answers (1)

Answer: (b)  x=\lambda x_{1}+(1-\lambda) \times, 0 \leq \lambda \leq 1 is an optimal solution.

Hint: As per known condition

Given: \text {x}_{1} and \text {x}_{2} are optimal solution.

Solution:

A set A_{1} is convex if, for any two points x_{1}, x_{2} \in A \text { and } \lambda \in[0,1] imply that \lambda x_{1}+(1-\lambda) x_{2} \in A

Since, here \text {x}_{1} and \text {x}_{2} are optimal solution.

Therefore, their convex combination will also be an optimal solution

Thus, option (b)  x=\lambda x_{1}+(1-\lambda) x, 0 \leq \lambda \leq 1 gives an optimal solution.

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