Hello! I need help answering the following questions:

Problem 1:

Frieda and her family live in Roanoke, Virginia, and they are planning an auto vacation across Virginia, their ultimate destination being Washington, DC. The family has developed the following network of possible routes and cities to visit on their trip: Winchester 5 Washington, DC 2 6 2 Staunton 2 Charlottesville 2 3 3 2 4 2 3 4 Richmond Roanoke The time, in hours, between cities (which is affected by the type of road and the number of intermediate towns) is shown along each branch. Determine the shortest route that the Millstone family can travel from Roanoke to Washington, DC.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 7 53 3 117 1 24 Roanoke 88 65 137 6 4 Petersburg Danville 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.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 4 190 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.The traffic management office in Richmond is attempting to analyze the potential traffic flow from a new office complex under construction to an interstate highway interchange during the evening rush period. Cars leave the office complex via one of three exits, and then they travel through the city streets until they arrive at the interstate interchange. The following network shows the various street routes (branches) from the office complex (node 1) to the interstate interchange (node 9): 4 2 0 2 0 5 7 8 7 3 3 4 4 0 3 2 0 6 1 2 5 3 6 0 5 6 All intermediate nodes represent street intersections, and the values accompanying the branches emanating from the nodes represent the traffic capacities of each street, expressed in thousands of cars per hour. Determine the maximum flow of cars that the street system can absorb during the evening rush hour.Given the following network, with activity times in weeks, determine the earliest and latest activity times and the slack for each activity. Indicate the critical path and the project duration: 3 15 1 10 4 Start 7 7 8 5 9 6 7 6 12