Come up with a list of five cities you would like to visit. Use the Internet to search for airline prices between these five cities. Make sure to include the city with the airport nearest your home from which you would start and end your trip.

(a) Draw a complete, weighted graph that represents these cities and the costs associated with flying between each pair of cities. 

(b) Use the brute force method to determine the optimal solution to visiting each city and returning home. 

(c) Use the nearest neighbor method to approximate the optimal solution.

(d) How much money does the optimal solution, obtained in part (b), save you over the approximation obtained in part (c)?