Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

-Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility?
A) 54
B) 56
C) 60
D) 65

Question

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.
 
-Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility?
A) 54 
B) 56 
C) 60 
D) 65

Quizplus · Accepted Answer

The minimum number of paths required to connect each facility, ensuring the preservation of natural beauty and minimizing construction time and cost, can be determined using the concept of a Minimum Spanning Tree (MST) in graph theory. The MST connects all points (facilities) with the least total edge (path) weight (distance). Without the specific distances between facilities provided, we can't calculate the exact MST value, but the question seems to imply a specific answer, suggesting a hypothetical or previously detailed scenario. Given the choices, the correct answer is chosen based on the assumption that the scenario's details lead to 54 as the minimum total distance in tens of yards to connect all facilities.

Consider the Following Network, Which Shows the Location of Various