Please Solve without using excel. A Excel solved answer is already there in chegg but i need it solved without excel as a linear programming model.

Please Thank you

(5) A steel mill in Gary supplies steel to manufacturers in eight other midwestern cities by truck, as shown in the following network: The travel time between cities, in hours, is shown along each branch. Use the Shortest Route Algorithm discuss in class, deter- mine the shortest route from Gary to each of the other eight cities in the network. Also, formulate the above shortest route problem as a linear programming problem. Define a decision variable for each branch in the network. Identify the objective function as well as all the constraints needed to formulate the problem as a linear programming problem. Detroit Cleveland 6 2 7 Toledo 3 Gary 4.5 5 9 3 2.5 4 Pittsburgh 4 3 8 3.5 Columbus 3 5 Ft. Wayne 3 N 6 3 3 Indianapolis Cincinnati