What kind of optimization problem is that? I am new here as a writer but I read this group from time to time.
I am thinking about the following problem.



Problem description:

Assume we have an area $A$ of size $1000 \times 1000$ cells.
One cell is addressed with $(x,y)$ pair, where $x$ and $y$ are positive integers.
We are given the set of points (locations) on area $A$, lets say we have $N$ locations. These locations are fixed and given as an input. In practice N is lower than 1000.
In each location we can build a sender station that sends some signal. Sender stations can have 4 levels: 0,1,2,3. Building a sender station with proper level costs: $c_0=0$, $c_1&gt;0$, $c_2&gt;c_1$ and $c_3&gt;c_2$ respectively. Costs are equal for each location. Moreover costs are fixed and given as an input. Each sender station covers given circular area with signal. Radius are following: $r_0=0$, $r_1&gt;0$, $r_2&gt;r_1$, $r_3&gt;r_2$. Radius is fixed and given as an input.

Question: What level of sender station should be build in each location in such a way, that: all locations are covered with signal and the total cost of building is minimized?



My question to that is: what kind of theoretical problem is that? Is there some easy transformation to some well known optimization problem?

This is not a homework from university, just my own riddle :)
As pointed out in the comments already, this is an instance of weighted geometric set cover. Here are some recent relevant references: 
http://www.divms.uiowa.edu/~kvaradar/paps/weightedcover.pdf 
See also the follow up work:
http://www.cs.uwaterloo.ca/~tmchan/cover_soda.pdf