<｜begin▁of▁sentence｜>### Instruction:
Suppose you are the lead sound engineer for a live concert featuring various music bands. You have an audio connectivity diagram which represents different connection points (nodes), cables (edges), and their capacity to carry sound signals measured in decibels (capacities). The nodes are the mixer (x), primary microphone (a), secondary microphone (b), guitar (c), keyboard (d), drums (e), and the main speaker system (y). 

Now, each connection has a different capacity: mixer to primary microphone (x to a) is 3.0 dB, mixer to secondary microphone (x to b) is 1.0 dB, primary mic to guitar (a to c) is 3.0 dB, secondary mic to guitar (b to c) is 5.0 dB, secondary mic to keyboard (b to d) is 4.0 dB, keyboard to drums (d to e) is 2.0 dB, guitar to main speaker (c to y) is 2.0 dB, and drums to main speaker (e to y) is 3.0 dB.

Your task is to figure out the loudest sound (maximum flow of audio signals) that can be transmitted from the mixer (source) to the main speaker system (sink) without overloading any cable (edge). How would you represent the flow of sound signals on each connection in this audio network?
### Response:
import networkx as nx

# Create a directed graph
G = nx.DiGraph()

# Add edges to the graph along with their respective capacities
G.add_edge('x', 'a', capacity=3.0)
G.add_edge('x', 'b', capacity=1.0)
G.add_edge('a', 'c', capacity=3.0)
G.add_edge('b', 'c', capacity=5.0)
G.add_edge('b', 'd', capacity=4.0)
G.add_edge('d', 'e', capacity=2.0)
G.add_edge('c', 'y', capacity=2.0)
G.add_edge('e', 'y', capacity=3.0)

# Find the maximum flow between 'x' (source) and 'y' (sink)
flow_value, flow_dict = nx.maximum_flow(G, 'x', 'y')

# Output the results
print('Flow value:', flow_value)
print('Flow dictionary:')
for u, v_flows in flow_dict.items():
    for v, flow in v_flows.items():
        print(f'{u} -> {v}: {flow}')
<|EOT|>
