Photo AI
The network diagram shows a series of water channels and ponds in a garden - HSC - SSCE Mathematics Standard - Question 30 - 2020 - Paper 1
Question 30
The network diagram shows a series of water channels and ponds in a garden. The vertices A, B, C, D, E and F represent six ponds. The edges represent the water chann... show full transcript
Worked Solution & Example Answer:The network diagram shows a series of water channels and ponds in a garden - HSC - SSCE Mathematics Standard - Question 30 - 2020 - Paper 1
Step 1
Determine the maximum flow of the network.
Answer
To determine the maximum flow of the network, we can use the method of finding the maximum flow through the stated paths.
By analyzing the capacities along the paths,
- Route from A to F can be broken down into:
- A to B (capacity 350)
- B to D (capacity 125)
- D to E (capacity 50)
- E to F (capacity 300)
- Route from A to C can be broken down into:
- A to C (capacity 200)
- C to E (capacity 100)
- E to F (capacity 300)
Calculating the bottlenecks:
- The maximum flow possible is determined by the path through BD, BE, CE, and CF, with total capacities leading to a maximum flow of:
Maximum flow = 275
Step 2
Is the cut shown a minimum cut? Give a reason for your answer.
Answer
To determine if the cut shown is a minimum cut, we need to evaluate the weight of the cut. The weight of the cut can be calculated by summing the capacities of the edges that the cut crosses:
Weight of cut = 200 (A to C) + 75 (B to D) + 50 (B to E) = 325.
Since this value (325) is greater than the maximum flow found earlier (275), the cut is not equal to the value of the maximum flow. Thus, the cut shown is not a minimum cut.