Algorithm to determine minimum server required?
This answer assumes that what you're trying to minimize is
$$
 \sum_{i \in S} c_i + \sum_{i=1}^n d(i,S),
$$
where $c_i$ is the cost of the $i$th server and 
$$d(i,S) = \min_{\substack{j \in S \\ j \geq i}} \; j-i$$
is the distance from $i$ to the closest server.

Use dynamic programming. For all $j \leq j_0$, compute the minimum of
$$
 \sum_{i \in S} c_i + \sum_{i=j}^n d(j,S)
$$
over all $S \subseteq \{j,\ldots,n\}$ such that $\min S = j_0$.