New firefighter stations shall be build in a municipality that will take care of 6 locations altogether. There are 6 possible places for the stations. The following list describes the sphere of action (locations) of the potential firefighter stations:
Place | A B C D E F
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Location | 1,2,5 2,3,4 1,4 2,3,6 1,4,6 4,5
The municipality is interested in building as few as possible stations in order to keep the building costs as low as possible. Formulate a linear optimization task which modellises the described problem.
I call A,B,C,D,E,F as $x_1,x_2,x_3,x_4,x_5,x_6$.
This is my objective function: $x_1+x_2+x_3+x_4+x_5+x_6 \rightarrow \text{ min }$
and these are my constraints:
$x_1+x_3+x_5 \leq 6$
$x_1+x_2+x_4 \leq 6$
$x_2+x_4 \leq 6$
$x_2+x_3+x_5+x_6 \leq 6$
$x_1+x_6 \leq 6$
$x_4+x_5 \leq 6$
Big thanks to @Marcello Sammarra for the comment!
Is my solution correct now?