3. The Roanoke, Virginia, distributor of Rainwater Beer delivers beer by truck to stores in six other Virginia cities, as shown in the following network: Staunton Charlottesville 2 31 5 Richmond 85 Lynchburg 61 72 53 3 117 1 24 Roanoke 88 65 137 6 4 Petersburg The mileage between cities is shown along each branch. Determine the shortest truck route from Roanoke to each of the other six cities in the network.4. The plant engineer for the Bitco manufacturing plant is designing an overhead conveyor system that will connect the distribution/inventory center to all areas of the plant. The network of possible conveyor routes through the plant, with the length (in feet) along each branch, follows 120 160 2 5 80 50 210 140 190 40 130 3 50 6 Determine the shortest conveyor route from the distribution/inventory center at node 1 to each of the other six areas of the plant