Question 10 12 pts The following diagram shows a general network N with lower and upper capacities. An initial flow is given as such that the numbers next to each arc are the lower capacity, the values of the flow through the arc, and the upper capacity of the arc 147 B 0212 0.15 006 15.15 2.25 se 12, 0 0 0.101638 125 2.4.16 119 0.27 F 128 G (a) Write down the value of the current flow from Sto T. The value of the current flow is: (b) Starting with the initial flow, use the maximum flow algorithm to find a maximum flow from Sto T and draw a diagram to indicate the flow along each arc. The value of your maximum flow is: (c) Find a minimum cut. A minimum cutis: (Key-in the edges in alphabetical order. Eg AB, DC, FE]) with capacity (d) If the upper capacity of arc EF increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (e) If the upper capacity of arc EF decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (f) If the upper capacity of arc AB increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (g) If the upper capacity of arc AB decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T. (Explain you answer briefly.) Question 10 12 pts The following diagram shows a general network N with lower and upper capacities. An initial flow is given as such that the numbers next to each arc are the lower capacity, the values of the flow through the arc, and the upper capacity of the arc 147 B 0212 0.15 006 15.15 2.25 se 12, 0 0 0.101638 125 2.4.16 119 0.27 F 128 G (a) Write down the value of the current flow from Sto T. The value of the current flow is: (b) Starting with the initial flow, use the maximum flow algorithm to find a maximum flow from Sto T and draw a diagram to indicate the flow along each arc. The value of your maximum flow is: (c) Find a minimum cut. A minimum cutis: (Key-in the edges in alphabetical order. Eg AB, DC, FE]) with capacity (d) If the upper capacity of arc EF increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (e) If the upper capacity of arc EF decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (f) If the upper capacity of arc AB increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T? (Explain you answer briefly.) (g) If the upper capacity of arc AB decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from Sto T. (Explain you answer briefly.)
