A major hotel chain $is$ constructing a new resort hotel complex $in$ Greenbranch Springs, West

Virginia. The resort $isin$ a heavily wooded area, and the developers want $to$ preserve $as$ much $of$

the natural beauty $as$ possible. $Todoso,$ the developers want $to$ connect all the various facilities $in$

the complex with a combination walking$-$riding path that will minimize the amount $of$ pathway

that will have $tobe$ cut through the woods. The following network shows possible connecting

$bpaths$ and corresponding distances $(in$ yards$)$ between the facilities:

Ignore Nodes $6-8$ and consider the remaining sub$-$network $-$ part $of$ the network consisting ofNodes $1-5.$ Formulate a mathematical program $to$ determine the path that will connect allthe facilities $in$ the above sub$-$network with minimum amount $of$ construction. Explicitlywrite all the constraints $in$ terms $of$ your decision variables $(notin$ terms $of$ generic setnotationsSandVas $on$ the lecture slides$).$

$(c)$ Use Excel solver $to$ solve the mathematical program formulated $in$ part $(b).$ Clearly describethe optimal path and corresponding pathway length.

$(d)$ Use Gurobi Python solver $to$ solve the mathematical program formulated $in$ part $(b).$Clearly describe the optimal path and corresponding pathway length$\mathrm{.}2$