A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if Find a solution using the nearest-neighbor method.

Question

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if  Find a solution using the nearest-neighbor method. ​ 
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Quizplus · Accepted Answer

Using the nearest-neighbor method, starting from New York we would visit Boston next (distance of 215 miles), followed by Washington, D.C. (distance of 225 miles), and then Cleveland (distance of 389 miles). The total distance traveled would be 215 + 225 + 389 = 829 miles. However, we still need to return to New York, so we would need to add another 215 miles to the total. Therefore, the shortest trip would be 829 + 215 = 1,044 miles. However, we must keep in mind that the nearest-neighbor method does not necessarily give us the optimal solution, so there could be a shorter trip that does not follow the nearest-neighbor approach.

A Saleswoman Wants to Visit Eastern Cities, New York City