Develop a linear programming model that can be used to find the minimum time required to make a delivery from location $1$ to location $6.($Express your answers in the form xij, where each xij represents the arc from node i to node j as either $1$ or $0.).$

a$)$ Min $35$X$12+30$X$13+...?$ Complete the rest of the model.

b$)$ What are the nodes $1$ through $6$ flows? $[$state each node flows individually$[$list flow$-$in and flow$-$out for each node$].$

How long $($in minutes$)$ does it take to make a delivery from location $1$ to location $6?($Round your answer to the nearest whole number.$)$

c$)$Assume that it is now $1$:$00$ p$.$m$.$ and that CARD just received a request for a pickup at location $1.$ The closest CARD courier is $8$ minutes away from location $1.$ If CARD provides a $20\%$ safety margin in guaranteeing a delivery time, what is the minimum guaranteed delivery time if the package picked up at location $1$ is to be delivered to location $6?($Enter your answer in standard time. Round your answer to the nearest minute.$)$