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There are multiple routes to reach from node 1 to node 2, as shown in the network. The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs. 200, and is Rs. 100 for the other toll booths. Which is the cheapest route from node 1 to node 2?

There are multiple routes to reach from node 1 to node 2, as shown in the network. The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs. 200, and is Rs. 100 for the other toll booths. Which is the cheapest route from node 1 to node 2? Correct Answer 1-f-b-2

Option 1: 1-a-c-2

Route

1 → a

a → c

c → 2

Cost

200

100

100

Total cost = 200 + 100 + 100 = 400

Option 2: 1-f-b-2

Route

1 → f

f → b

b → 2

Cost

100

0

200

Total cost = 100 + 0 + 200 = 300

Option 3: 1-b-2

Route

1 → b

b → 2

Cost

300

200

Total cost = 300 + 200 = 500

Option 4: 1-f-e-2

Route

1 → f

f → e

e → 2

Cost

100

100

200

Total cost = 100 + 100 + 200 = 400

Therefore, the cheapest route from node 1 to node 2 is 1-f-b-2.

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