Choosing $n$-dimensional column vector $x$ to maximize $ax$ s.t. $Bx \leq c$ and $x \geq 0$, where $a$ is an $n$-dimensional row vector, $B$ an $m\times n$ matrix, and c an $m$-dimensional row vector. Let the lagrangian be $L(x,\lambda)=ax+\lambda(c-Bx)$, where $\lambda$ is an $m$-dimensional vector of multipliers.
Show that if $\bar{x}$ is a solution, with the corresponding vector of multipliers $\bar{\lambda}$, then $$L(x,\bar{\lambda}) \leq L(\bar{x},\bar{\lambda}) \leq L(\bar{x},\lambda) \quad \forall x \geq 0 \text{ and } \lambda \geq 0.$$
This question is as part of my optimization class and we barely talked about linear programming. So, I would appreciate any help.