Consider the following network for answering the following parts.(a) Suppose that the nodes represent cities where the distributors of a certain firm are located, and the values on the arcs denote distances (in miles) between the cities. Formulate a mathematical model that will yield the shortest route for a sales representative of the retail distributor in City 1 to travel to City 10 , in which a meeting will be held with the attendance of all sales representatives.(b) Apply the total enumeration approach to solve the problem mentioned in part (a).(c) To find the shortest route mentioned in part (a), an equivalent network with reduced size can be obtained by decreasing the number of cities. This is possible by removing some of the cities without disturbing the connections among the cities. Make this reduction, draw the new network, and write the revised mathematical model for solving the same problem in part (a).(d) The firm is now considering a communication system between the firm’s center in City 6 and each retail distributor. Considering the original given network, formulate a mathematical model to determine a single interconnecting path to all distributors that will result in the smallest number of miles. What type of network problem is described above?(e) Now assume that the values on the arcs in the given original network denote the flow capacities (maximum number of units of a product that can be sent) between cities. Formulate a mathematical model to determine maximum number of units that can be sent from City 1 to City 10. What type of network problem is described above? Without solving the mathematical model, examine the given original network and determine the maximum number of units that can be sent from City 1 to City 10.Note: In formulating the mathematical models, first define the decision variables, next write the objective function and constraints in OPEN mathematical form and finally explain them clearly.
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