# MATH 1025: EXPLORING MATHEMATICS IN THE EVERYDAY WORLD

## Assignment 1: Exploration Activity: I Found the Cheaper Route

The ability to understand how you can find the shortest route or cheapest rate for travel can be beneficial in real life. For this week’s Exploration Activity, you will create and solve a traveling salesperson problem.

**To prepare for this Assignment:**

- Choose four cities you would like to visit.
- Consult the Internet and use one-way airfares between cities to create a weighted graph.

##### By Day 6

**Assignment (1–2 pages including the images):**

- Assume that you are located at A. Let B, C, D, and E represent each of the four cities you have chosen.
- Use the Brute Force Method to find the optimal solution to visiting each of our chosen cities and returning home. Show all your work.
- Use the Nearest Neighbor Method to approximate the optimal solution. Show all your work.
- Identify how much money is being saved by using the optimal solution instead of the approximation. Show all your work.
- Clearly label your work and identify each of the methods.
- Put all of your work into one document.
- Include all the resources that you used.

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## Exploration Activity: I Found the Cheaper Route

The ability to understand how you can find the shortest route or cheapest rate for travel can be beneficial in real life. For this week’s Exploration …