PART $1$: PROBLEM SOLVING $(40$ Marks$)$

Directions: Solve all the requirement of the problems. Show your solutions.

$1-$ The graph below is is anetwork representing ten houses that a telecommunications company wants to connect using the minimum cable length $($ the numbers on the arcs are the distances between houses in meters$).(15$ marks$)$

A$-$ Design a network model using the minimal$-$spanning tree technique to determine the path through the network that connects all the houses while minimizing total distance $($minimal total cable length$).$

Summarize your steps in a table showing the:

a$.$ Connected nodes b$.$ Unconnected nodes c$.$ Closest unconnected node d$.$ Arc Selected e$.$ Arc length f$.$ Total Distance

B$-$ Compute the minimal total distance.

Rubrics for marking:

$2$ mark $=$ Finding connected nodes

$2$ mark $=$ Finding the arc selected

$2$ mark $=$ Finding unconnected nodes

$2$ mark $=$ Finding the arc length

$2$ mark $=$ Finding closet connected nodes

$2$ mark $=$ Finding the total distance

$3$ marks $=$ Compute the minimal total distance