Question

you have three errands to run around town, although in no particular order. you plan to start and end at home (h). you must go to the bank (b), the post office (p), and the market (m). distances, in miles, between any two of these locations are given in the table. use the nearest neighbor method to approximate the shortest route to run your errands and return home. what is the minimum distance given by the hamilton circuit? how does the circuit compare to the hamilton circuit found using the brute force method, h, b, p, m, h, with a distance of 15.4? using the nearest neighbor method, the shortest route is with a distance of miles. the two circuits are (use a comma to separate vertices as needed. type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Start at Home (H)

From home, the nearest neighbor is Market (M) with distance \(3.5\) miles.

Step2: From Market (M)

From market, the nearest neighbor is Bank (B) with distance \(5\) miles.

Step3: From Bank (B)

From bank, the nearest neighbor is Post - Office (P) with distance \(3.8\) miles.

Step4: From Post - Office (P)

From post - office, return to Home (H) with distance \(5.5\) miles.

The total distance is \(3.5+5 + 3.8+5.5=17.8\) miles.

Answer:

Using the Nearest Neighbor Method, the shortest route is \(H,M,B,P,H\) with a distance of \(17.8\) miles. The two circuits: the circuit from Nearest Neighbor Method (\(17.8\) miles) is longer than the circuit from Brute - Force Method (\(15.4\) miles).