A$)$ Given this data model the problem to calculate the shortest path from point $0($gebze$)$ to point $6($Graz$,$ Austria$).$ Do not find the solution just model the problem, as an LP$.$

B$)$ Discuss how would you update the model in part $($a$)$ if the trucking company is concerned with the time. The company wants not the shortest path but the fastest path from Gebze to Graz. What other parameters do you need for this model? Assume that data related those parameters are also available, update the model so that it will optimizes the travel time from Gebze to Milano. Hint: for this case, do not use actual values but give symbolling names for the related data $($e$.$g$.,$ wi for wait times, sij for speed between i and j nodes, etc.$)$

C$)$ If the trucking company wants to optimize the trip both in regard to time and distance, what do you recommend them. Give a sketch of the new model, do not need to provide the whole model.