Is the language in the description context free?
The basic problem here is that context-free languages are not closed under intersection. 

The example you give illustrates this. Thus, $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b\}$ is context-free, and similarly, so is $\{ w\in\{a,b,c\}^* \mid |w|_b \le |w|_c\}$. The intersection of these two languages $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b \le |w|_c\}$ is not context-free.