1. In the network below (See Fig. 1), the demand values are shown on vertices (supply values are negative). Lower bounds on flow and edge ca- pacities are shown as (lower bound, capacity) for each edge. Determine if there is a feasible circulation in this graph. Please complete the following steps. (A:6 (2,5) (E:-4 (5,7) (3, 8) (1,4) B:5 (4,8) (D:-4) Figure 1 (1,9) (2,5) (C:-3 (a) Remove the lower bounds on each edge. Write down the new demands on each vertex A, B, C, D, E, in this order.
1. In the network below (See Fig. 1), the demand values are shown on vertices (supply values are negative). Lower bounds on flow and edge ca- pacities are shown as (lower bound, capacity) for each edge. Determine if there is a feasible circulation in this graph. Please complete the following steps. (A:6 (2,5) (E:-4 (5,7) (3, 8) (1,4) B:5 (4,8) (D:-4) Figure 1 (1,9) (2,5) (C:-3 (a) Remove the lower bounds on each edge. Write down the new demands on each vertex A, B, C, D, E, in this order.
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Transcribed Image Text:1. In the network below (See Fig. 1), the demand values are shown on
vertices (supply values are negative). Lower bounds on flow and edge ca-
pacities are shown as (lower bound, capacity) for each edge. Determine if
there is a feasible circulation in this graph. Please complete the following
steps.
(2,5)
A:6
(E:-4
(5, 7)
(3,8)
(1,4)
B:5
(4,8)
D:-4
Figure 1
(1,9)
(2,5)
(C:-3
Remove the lower bounds on each edge. Write down the new demands
on each vertex A, B, C, D, E, in this order.
(b) Solve the circulation problem without lower bounds. Write down the
max-flow value.
(c) Is there is a feasible circulation in the original graph? Explain your
answer.
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