Please show the complete manual step-by-step solution

MAXIMAL FLOW 0 Natural Gas Company distributes gas from its source in Node 1 through a network of pipelines and pumping stations to its main storage facility in Node 9. The table below gives the capacity per link in thousands of cubic feet/hour. Draw the network diagram. (5 points) Determine the maximum hourly volume that can be delivered to the main storage tank? Solve using augmenting paths. (15 points) Link Forward Reverse Flow Flow 1-2 10 0 1-3 5 0 1-4 9 2-4 6 4 2-5 3 3 3-5 7 6 3-6 8 4 3-7 5 1 4-7 2 0 4-8 18 5-8 13 5-9 7 0 6-7 5 6-8 6 7-8 14 7 7-9 10 0 8-9 5 0 9 6 8 MINIMAL SPANNING TREE RDB developer is planning a small residential community in Laguna consisting of stand-alone houses, row- houses, a commercial area, recreational facilities, a community center, a school, among others. The developer would like to connect the various residential areas and facilities using the minimum length of subdivision roads. The network below shows the possible roads in the development with the distance measured in thousand feet. Determine the shortest road network that connects the 10 areas. What is the total length of the roads? Use tabular method. 1 7 8 9 10 - - From/To 1 2 3 2 3 4 5 6 6.5 4.1 4.8 3.6 7.2 8.2 5.6 5.9 - | - A 7.8 6.3 4 5.5 5 - 2.1 - 6 2.8 3.4 2.7 M. 2.7 7 8 9 6.1 5.4 4.6 10 MAXIMAL FLOW 0 Natural Gas Company distributes gas from its source in Node 1 through a network of pipelines and pumping stations to its main storage facility in Node 9. The table below gives the capacity per link in thousands of cubic feet/hour. Draw the network diagram. (5 points) Determine the maximum hourly volume that can be delivered to the main storage tank? Solve using augmenting paths. (15 points) Link Forward Reverse Flow Flow 1-2 10 0 1-3 5 0 1-4 9 2-4 6 4 2-5 3 3 3-5 7 6 3-6 8 4 3-7 5 1 4-7 2 0 4-8 18 5-8 13 5-9 7 0 6-7 5 6-8 6 7-8 14 7 7-9 10 0 8-9 5 0 9 6 8 MINIMAL SPANNING TREE RDB developer is planning a small residential community in Laguna consisting of stand-alone houses, row- houses, a commercial area, recreational facilities, a community center, a school, among others. The developer would like to connect the various residential areas and facilities using the minimum length of subdivision roads. The network below shows the possible roads in the development with the distance measured in thousand feet. Determine the shortest road network that connects the 10 areas. What is the total length of the roads? Use tabular method. 1 7 8 9 10 - - From/To 1 2 3 2 3 4 5 6 6.5 4.1 4.8 3.6 7.2 8.2 5.6 5.9 - | - A 7.8 6.3 4 5.5 5 - 2.1 - 6 2.8 3.4 2.7 M. 2.7 7 8 9 6.1 5.4 4.6 10