Brute force logic what path should the salesman take to minimize the cost of the trip, calculus homework help

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The following chart shows the cost of traveling from one city to another (in dollars). A traveling salesman begins at Greenbrier, visits all the cities once, and returns to Greenbrier when done. According to the brute force method, what path should the salesman take to minimize the cost of the trip?

  Greenbrier Jamestown Oregon Dayton Xenia
Greenbrier – 557 305 399 379
Jamestown 557 – 626 305 335
Oregon 305 626 – 313 507
Dayton 399 305 313 – 532
Xenia 379 335 507 532 –

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