Case Problem


[Page 314 ( continued )]

T HE P EARLSBURG R ESCUE S QUAD

The Pearlsburg (West Virginia) Rescue Squad serves a mountainous, rural area in southern West Virginia. The only access to the homes , farms, and small crossroad communities and villages is a network of dirt, gravel, and poorly paved roads . The rescue squad had just returned from an emergency at Blake's Crossing, and two of the squad members , Melanie Hart and Ben Cross, were cleaning up and getting the truck back in proper order for the next call.

"You know, Ben," said Melanie, "that was close. We could have lost little Randy if we had been a few minutes later in getting to their farm."

"Yep," said Ben.

After a moment Melanie continued, "I was sort of wondering about the route Dave took to get there. It seems to me if we had gone around by Cedar Creek, we could have gotten there a few minutes sooner. And as close as things got, a few minutes could have made a big difference, don't you think?"

"Yep," said Ben.

"Well, I was wondering, Ben, 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 the quickest way to all the different places is?"

Ben thought a moment before answering. "It would take us a while to time all the different ways you could get from here to everywhere we go."

"That's true," Melanie answered , "but I've been studying a way to work out this sort of problem in one of my college courses. All we have to do is get the times it takes to travel each piece of road between all these little communities, and I think I can do the rest. Will you help me?"

"Sure," Ben said.

"Okay, then, here's what we'll do. I'll write down all the routes you should time, and I'll time the rest all the way over to Holbrook."

Here is the combined list of times (in minutes) Melanie and Ben compiled for all the route segments between Pearlsburg and Holbrook:


[Page 315]

Segment

Time

Pearlsburg to Kitchen Corner

10

Pearlsburg to Quarry

15

Pearlsburg 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 Wellis 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 Wellis Farm

9

Homer to Wellis Farm

11

Homer to McKinney Farm

8

McKinney Farm to Wellis Farm

21

Wellis Farm to Holbrook

10

Bottom Town to Holbrook

12


Determine the shortest routes from Pearlsburg to all the different communities and farms visited by the rescue squad.




Introduction to Management Science
Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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