$$\max \quad c \cdot x \\ \mathrm{s.t.} \ Ax \leq b\\ x\geq 0 \\$$
There are two optimal solutions to the LP $u$ and $v$. How do I show that for $\lambda \in [0,1]$, $\lambda u + (1-\lambda)v$ is also an optimal solution
- First, I have to show that $\lambda u + (1-\lambda)v$ has the same value of the objective function as $u$.
- Then show $\lambda u + (1-\lambda)v$ is a feasible solution.
For 1) how would I approach this problem and then show that $\lambda u + (1-\lambda)v$ is a feasible solution? Would appreciate any tips, help and explanation.