Minimum Spanning Tree: Premiere Bank will be connecting computer terminals at each one of its branch offices to the computer at its main office using a landcable system. A branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected $($directly or indirectly$)$ to the main office. The only requirement is that every branch office be connected by some route to the main office. The distance $($in miles$)$ between every pair of offices is shown below. $($a$)$ Describe how this problem fits the framework of the minimum spanning tree problem. $($b$)$ Draw an undirected graph for this problem. $($c$)$ Apply step$-$by$-$step Kruskal$$s Algorithm to solve it$.($d$)$ Verify your solution with Python.

A new airport being built will have three terminals and two baggage pickup areas.

An automated baggage delivery system has been designed to transport the baggage

from each terminal to the two baggage pickup areas. This system is depicted graphi$-$

cally in Figure $5\mathrm{.}43,$ where nodes $1,2,$ and $3$ represent the terminals, and nodes $7$ and

$8$ represent the baggage pickup areas. The maximum number of bags per minute that

can be handled by each part of the system is indicated by the value on each arc in the

network.

a$.$ Formulate an LP model to determine the maximum number of bags per minute

that can be delivered by this system. $($ Frown $1,2,3$ to $7,8)$

b$.$ Use Solver to find the optimal solution to this problem.