Suppose that we have the following cities: Mudville, Horns, Farm Town, Almira, Billows, Carmenovsk, Dantub. They are in a rural county and have no paved roads.

Your county government decides to build a paved network of roads to inter-connect these 7 cities. Engineers have estimated costs of building roads between any two towns from the above list. They came to the conclusion that some connecting roads would be prohibitively expensive, so settled on the roads below with the indicated costs in millions of dollars.

Altamira-Mudwille 15, Altamira FarmTown 10; Billows-Carmenovsk 1, Billows - Dantub 1, Billows - Horns 17; Carmenovsk-Dantub 1; Carmenovsk-FarmTown 12, Carmenovsk-Horns 5; Dantub-FarmTown 12; Farmtown-Homs 2; Horns-Mudville 2; You are the budget office director for the county, and have been given the responsibility of budgeting for the project. What is the minimum amount you have to budget? Justify your answer.

Perform the QuickUnion Weighted algorithm on the graph of problem 3, using Kruskal's algorithm. That is do the Unions and Finds in the order necessary for Kruskal.