I am new here as a writer but I read this group from time to time. I am thinking about the following problem.
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: $c_0=0$, $c_1>0$, $c_2>c_1$ and $c_3>c_2$ 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: $r_0=0$, $r_1>0$, $r_2>r_1$, $r_3>r_2$. 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 :)