Write down the mathematical model of $k-$center problem. k$-$center problem has the following setup: $($No partial points

will be given!$)(7\mathrm{.}5$ points$)$

$(1)n$ potential locations for facilities and in total $k$ centers are located,

$(2)$ n customers to serve,

$(3)$ the distance between locations are known, $D[i][j]$ denotes the distance between i and $j,$

$(4)$ each customer must be served by one center,

$(5)$ The objective is to locate k centers such that the maximum distance is minimized

Write down a mathematical optimization model of $k-$center problem. Define variables.

Suppose each customer has service demand of $D_1$ and at most $C$ units of service may be satisfied by a center. Update your

model accordingly. $(2\mathrm{.}5$ points$)$