Category: Mathematics homework help

  Unit 4, we are learning about the graph theory. For this discussion, you will post at least twice – 1) an initial post, and then 2) a reply to a classmate.
For your initial posting, based on the concepts from this unit, answer at least one of the following:
Share a thing that you learned about graph theory.
Share a resource you found that was helpful to your understanding of the concepts in this unit.
Ask a question about graph theory.
Post a relevant or encouraging meme about graph theory.

 
You are the vehicle dispatcher for a delivery service that serves a mix of ‘easy’ customers who are quite pleasant when the driver arrives and ‘hard’ customers who are difficult to manage. In order to keep the drivers happy, you never assign a driver to visit two hard customers in a row. Thus, for each driver, given a set of ‘easy’ and ‘hard’ customers to visit, your goal is to minimize the travel time to visit all customers, starting and returning from the company depot, satisfying the constraint that a hard customer visit cannot be followed by another hard customer.
This problem can be infeasible if the number of hard customers is greater than the number of easy customers. Let’s assume that this is sometimes the case. As dispatcher, you have decided to relax the constraint that a hard customer visit cannot be followed by another hard customer. Rather, you want to minimize the number of times this happens and minimize the route travel length.
It may not be possible to minimize both terms at once; how would you find a good compromise?
Formulate the Hard/Easy Customer Traveling Salesman Problem (TSP) with the two term objective function terms. Define any new notation you introduce and explain your formulation in words and present mathematically.
Develop a heuristic to solve the problem. Clearly present your heuristic.
Solve the instances posted in the excel file. Solutions should include the visit sequence of nodes and the tour length and # of times a hard customer follows another hard customer for each instance. Your solution should be included on the tab “Sample solution” in the data spreadsheet.

 
Charts and graphs are often used to present statistics in newspapers, magazines, books, and various online articles. There are pros and cons to using these types of visual representations.
Describe one pro and one con of using a graph or chart. Then, share an example of a time when a data visualization (like a graph or chart) changed your mind about something or gave you a deeper understanding of a topic or current event.

In this chapter, we learned how mortgages are used to help people purchase a home.
Please research at least two of the following topics and report your findings:
How do you “qualify” for a home mortgage, that is, what conditions must be met for a bank to approve your home loan?
What expenses do you need to budget for in addition to the mortgage payment itself?
What are the pros and cons of home buying vs. renting?
Directions
Participation in Discussion Boards is a required part of this class (5% of your overall course average).
The requirements for this graded Discussion Board are:
Your initial post is due by the 3rd day of the Discussion Board and must contain at least 100 words.
You must respond to at least two classmates, and your response posts must contain at least 50 words.
Please answer any questions posed in the instructor’s response to your post(s).
All posts should be relevant to the week’s topic(s) and should include substantive, correct math content.
All posts should be grammatically correct – please use Spellcheck as necessary.
Please use APA citation format if you get help from another source (our textbook, another book, a website, etc.). Try to use your own words!

Sep 15 – Sep 25
In this chapter, we learned about “weighted” graphs (graphs with numbers called “weights” on each of its edges), and we learned about two special types of weighted graphs:
Minimum Hamilton Circuit:  a circuit which visits each vertex in a graph exactly once (returning to the starting vertex) and which has the smallest total weight
Minimum Spanning Tree:  a subgraph of the original graph which is a tree, which includes all vertices in the original graph, and which has the smallest total weight
Please research and find an example of how one of these can be applied to solve a real-world problem and report your findings.
Directions
Participation in Discussion Boards is a required part of this class (5% of your overall course average).
The requirements for this graded Discussion Board are:
Your initial post is due by the 3rd day of the Discussion Board and must contain at least 100 words.
You must respond to at least two classmates, and your response posts must contain at least 50 words.
Please answer any questions posed in the instructor’s response to your post(s).
All posts should be relevant to the week’s topic(s) and should include substantive, correct math content.
All posts should be grammatically correct – please use Spellcheck as necessary.
Please use APA citation format if you get help from another source (our textbook, another book, a website, etc.). Try to use your own words!