e$)$ Military commanders are planning the command structure for $6$ new radar stations. Three commanders will each be in charge of two stations. The following table shows the projected cost $($in millions of $)$ of building the necessary communication links between jointly commanded locations.

$23456$

$14265293155$

$220394021$

$3685522$

$43039$

$547$

Planners seek a minimum cost way to organise the command. Formulate this problem as an Integer Linear Programme and clearly explain decision variables, objective function and constraints. $($You don$$t need to solve the model.$)$