INCLUDE SCREESNHOT OF EXCEL WORK, INCLUDING ALL FORMULAS AND SOLVER INPUTS

Freedom County consists of six towns that need emergency ambulance service. A station at a town can serve other towns within $18$ minutes $($less than or equal to $18)$ of driving time. The table below gives the driving times in minutes among the six towns.

$\backslash$table$[[$Time in minutes from town i to j$],[$i$$j$,1,2,3,4,5,6],[1,0,19,23,18,20,25],[2,19,0,22,13,22,11],[3,23,22,0,60,17,20],[4,18,13,60,0,55,17],[5,20,22,17,55,0,12],[6,25,11,20,17,12,0]]$

Assuming stations can only be built in these six towns $($not in between$),$ do the following:

a$)[10$pt$]$ Formulate an integer linear programming problem mathematically to find the smallest number of stations that will serve all towns. Clearly define the decision variables, objective and constraints.

Station at $1$ can serve: $1,4_{?}$ etc.

b$)[10$pt$]$ Solve the integer linear programming problem defined in part a$)$ using Excel's solver or Python's linprog function. Report the number and locations of the service stations at the optimum.