2. (35pts) A utility manager in Denver wants to determine a flow plan wants to determine a flow plan that will maximize the flow of water into the city. Water flows into the city through a system of aqueducts that originate at three rivers (A, B, and C) through various junction points (1 through 6) that terminate in Denver. The table below shows the maximum amount of water (in thousands of acre feet) that can be pumped through each aqueduct per day. Aqueduct A to 1 A to 2 B to 1 B to 2 B to 3 C to 2 C to 3 1 to 4 1 to 5 2 to 4 2 to 5 2 to 6 3 to 5 3 to 6 4 to Denver 5 to Denver 6 to Denver Capacity (x 1,000acre feet) 75 65 40 50 60 80 70 60 45 70 55 45 70 90 120 190 130 a) Draw a network flow model for this problem. b) Create a spreadsheet model for this problem to find an optimal flow plan