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(B) In a Linear Programming $(LP)$ problem,the feasible region is a convex set.If $x$ and $y$ are two optimal solutions,then the objective function va

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$z=\lambda x+(1-\lambda) y, 0 \leq \lambda \leq 1$ is also an optimal solution.

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(B) In a Linear Programming $(LP)$ problem,the feasible region is a convex set.If $x$ and $y$ are two optimal solutions,then the objective function value at these points is the same,say $Z^*$.Since the objective function is linear,for any convex combination $z = \lambda x + (1 - \lambda) y$ where $0 \leq \lambda \leq 1$,the value of the objective function is:$f(z) = f(\lambda x + (1 - \lambda) y) = \lambda f(x) + (1 - \lambda) f(y) = \lambda Z^* + (1 - \lambda) Z^* = Z^*$.Thus,any convex combination of two optimal solutions is also an optimal solution.

Let $x$ and $y$ be optimal solutions of a Linear Programming $(LP)$ problem. Then,which of the following is true?

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