3. (28 pts) A bank will be hooking up computer terminals at each of its branch offices to the computer at its main office, using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is directly proportional to the mileage involved, where the distance (in miles) between every pair of offices is as follows: Main B.1 190 Main office Branch 1 Branch 2 Branch 3 Branch 4 Branch 5 190 70 115 270 160 Distance between Pairs of Offices B.2 B.3 B.4 70 115 270 100 110 215 140 120 140 175 120 175 220 80 310 B.5 160 50 220 80 310 100 110 215 50 Management wishes to determine which pairs of offices should be directly connected by special phone lines in order to connect every branch office (directly or indirectly) to the main office at a minimum total cost. a. Model this problem as a network problem (which problem should be solved on which network?). b. Find the optimal solution and the related cost. Explain briefly the method used