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.
Related questions
Question
Figure 1
(a) 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.
**Graph Explanation:**
The graph in Figure 1 shows five vertices: \(A\), \(B\), \(C\), \(D\), and \(E\) with respective demand or supply values:
- \(A: 6\)
- \(B: 5\)
- \(C: -3\)
- \(D: -4\)
- \(E: -4\)
The directed edges between these vertices have specified lower bounds and capacities. For example, from \(A\) to \(B\) the lower bound and capacity is \((5, 7)\).
Edges are drawn with directed arrows indicating the direction of flow, with the following details:
- \(A\) to \(B\): \((5, 7)\)
- \(A\) to \(E\): \((2, 5)\)
- \(B\) to \(C\): \((1, 9)\)
- \(C\) to \(E\): \((2, 5)\)
- \(A\) to \(D\): \((3, 8)\)
- \(D\) to \(B\): \((4, 8)\)
- \(E\) to \(D\): \((1, 4)\)
The objective is to check the feasibility of circulation by removing lower bounds initially, adjusting demands, and calculating potential maximum flow.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2159a2e8-e3dc-49a1-958f-4531490b4ad7%2Fdec6d9f6-2366-4c5a-9683-4fdee6b8cdb0%2Fkfyq3nk_processed.png&w=3840&q=75)
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 capacities are shown as (lower bound, capacity) for each edge. Determine if there is a feasible circulation in this graph. Please complete the following steps.
Figure 1
(a) 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.
**Graph Explanation:**
The graph in Figure 1 shows five vertices: \(A\), \(B\), \(C\), \(D\), and \(E\) with respective demand or supply values:
- \(A: 6\)
- \(B: 5\)
- \(C: -3\)
- \(D: -4\)
- \(E: -4\)
The directed edges between these vertices have specified lower bounds and capacities. For example, from \(A\) to \(B\) the lower bound and capacity is \((5, 7)\).
Edges are drawn with directed arrows indicating the direction of flow, with the following details:
- \(A\) to \(B\): \((5, 7)\)
- \(A\) to \(E\): \((2, 5)\)
- \(B\) to \(C\): \((1, 9)\)
- \(C\) to \(E\): \((2, 5)\)
- \(A\) to \(D\): \((3, 8)\)
- \(D\) to \(B\): \((4, 8)\)
- \(E\) to \(D\): \((1, 4)\)
The objective is to check the feasibility of circulation by removing lower bounds initially, adjusting demands, and calculating potential maximum flow.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
