<｜begin▁of▁sentence｜>### Instruction:
Suppose we have a network with four nodes, where 'a' wants to send 5 units of a commodity and 'd' wants to receive 5 units. The network has edges between 'a' to 'b' and 'a' to 'c' with different costs and capacities, and edges from 'b' to 'd' and 'c' to 'd' to deliver to 'd'. What is the flow cost to satisfy all demands with minimum cost, and how is the flow distributed among the edges?
### Response:
import networkx as nx

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

# Add nodes with their demand
G.add_node('a', demand=-5)
G.add_node('d', demand=5)

# Add edges with weights and capacities
G.add_edge('a', 'b', weight=3, capacity=4)
G.add_edge('a', 'c', weight=6, capacity=10)
G.add_edge('b', 'd', weight=1, capacity=9)
G.add_edge('c', 'd', weight=2, capacity=5)

# Run the network simplex algorithm
flowCost, flowDict = nx.network_simplex(G)

# Display the cost of the flow and the flow on each edge
print('Flow Cost:', flowCost)
print('Flow Dict:', flowDict)
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