this is my 3rd time posting this question. please don\'t give me the same answer

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this is my 3rd time posting this question. please don't give me the same answer in the chegg textbook solutions, it's not correct. solve by hand and find the shortest route from the hotel to EACH of the 9 destinations. again, the textbook solution on Chegg is not helpful. find by listing the permanent sets.

A Hotel has a limousine van that transports guests to various business and tourist locations around the city. The following network indicates the different routes the limousine could follow from the hotel at node 1 to the nine locations (nodes 2 through 10):

The values on each branch in the network are the distances, in miles, between the locations.
Determine the shortest route from the hotel to each of the nine destinations . (Please show Detailed steps)

this is my 3rd time posting this question. please don't give me the same answer in the chegg textbook solutions, it's not correct. solve by hand and find the shortest route from the hotel to EACH of the 9 destinations. again, the textbook solution on Chegg is not helpful. find by listing the permanent sets.

Explanation / Answer

Firstly we must note that in this diagram, the direct route is mostly the shortest route. E.g 4-7 is shorter than 4-6-7. This is only violated in 2 conditions -

1) 4-5 is longer than 4-3-5

2) 2-6 is longer than 2-4-6.

Knowing this will help us in cutting down sets. Now lets find the shortest routes -

1) 1-2 :

Here the shortest route is 1-2 itself

2) 1-3

Here the shortest route is 1-3 itself

3) 1-4

Here the shortest route is 1-4 itself

Now, the easiest ones are done, lets move to complicated ones

4) 1 - 5

two feasible route sets are : 1-4-5 and 1-3-5. The shortest one is 1-3-5, due to the anomaly mentioned above.

5) 1-6

Feasible sets are : 1-2-6, 1-2-4-6, 1-4-6. Calculating the distance, 1-4-6 is the shortest

6) 1-7

Here the shortest route is 1-4-7 itself becasue as we mentioned direct route is shortest except for the above anomalies.

7) 1-8

Using law that direct route is shortest,

possible solutions are :1-2-4-6-9-8, 1-3-5-8.

The shortest route in distance is 1-3-5-8

8) 1-9

Since 9 can be reached from 6 or 7 or 8, the 3 possible routes are : 1-4-6-9, 1-4-7-9, 1-3-5-8-9.

The shortest route is 1-4-6-9

9) 1-10.

10 can be reached from 8 or 9. so possible routes are : 1-4-6-9-10 or 1-3-5-8-10

1-4-6-9-10 is the shortest route on calculation

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