The sketch below shows a network of highways connecting 9 towns. Identify the sample space of all possible routes between towns 1 and 9. Follow the arrows.  The possible travel times for each leg of the journey are indicated on the sketch. What is the shortest possible (total) travel time between towns 1 and 9? Report the time and the corresponding route. What is the sample space of travel times for route 1 → 2 → 9?

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Chapter1: Combinatorial Analysis
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The sketch below shows a network of highways connecting 9 towns.

  1. Identify the sample space of all possible routes between towns 1 and 9. Follow the arrows. 
  2. The possible travel times for each leg of the journey are indicated on the sketch. What is the shortest possible (total) travel time between towns 1 and 9? Report the time and the corresponding route.
  3. What is the sample space of travel times for route 1 → 2 → 9?
Possible Travel Times
3, 4, 5 hr
9.
2.
1, 2 hr
1, 1.5
(3
1.5, 2
0.5, 1
7
Start
1, 1.5
1, 2
4
1.5, 2.5
6.
0.5
2, 3
Transcribed Image Text:Possible Travel Times 3, 4, 5 hr 9. 2. 1, 2 hr 1, 1.5 (3 1.5, 2 0.5, 1 7 Start 1, 1.5 1, 2 4 1.5, 2.5 6. 0.5 2, 3
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Given,

The diagram for a network of highways connecting 9 towns.

 

 

 

 

To  find,

a. Identify the sample space of all possible routes between towns 1 and 9. Follow the arrows. 

b. The possible travel times for each leg of the journey are indicated on the sketch. What is the shortest possible (total) travel time between towns 1 and 9? Report the time and the corresponding route.

c. What is the sample space of travel times for route 1 → 2 → 9?

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