Tom and Bryan would like to visit a rural area in Country XYZ with only access to

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Question:

Tom and Bryan would like to visit a rural area in Country XYZ with only access to homes, farms, and small crossroad communities and villages is a network of dirt, gravel and poorly paved roads. Blake was wondering, “why don’t we study all these different ways to get to the little communities and farms around here so we will always know what is the quickest way to all the different place is.” Bryan agreed and then spent a lot of time with Tom to study all the different routes and times it takes to travel to each communities and farms. Below is the list of times (in minutes) they compiled for all the route segments.

Pearls to Kitchen Corner 10

Pearls to Quarry 15

Pearls to Morgan Creek 12

Kitchen Corner to Cutter’s Store 20

Kitchen Corner to Stone House 14

Kitchen Corner to Quarry 8

Quarry to Blake’s Crossing 18

Quarry to Cedar Creek 9

Morgan Creek to Quarry 16

Morgan Creek to Cedar Creek 7

Morgan Creek to Homer 18

Morgan Creek to McKinney Farm 11

Stone House to Cutter’s Store 10

Stone House to Blake’s Crossing 6

Cedar Creek to Blake’s Crossing 10

Cedar Creek to Willis Farm 17

Cedar Creek to Homer 5 Cutter’s Store to Blake’s Crossing 12 Cutter’s Store to Bottom Town 14 Blake’s Crossing to Bottom Town 6 Blake’s Crossing to Holbrook 15 Blake’s Crossing to Willis Farm 9 Homer to Willis Farm 11 Homer to McKinney Farm 8 McKinney Farm to Willis Farm 21 Willis Farm to Holbrook 10 Bottom Town to Holbrook 12

(a) Represent the above information in a network diagram.

(b) Determine the shortest time to visit all the different communities and farms from Pearls using

(i) shortest route algorithm

(ii) minimal spinning tree algorithm