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Simplex Method is an application developed for an assignment of a Linear Programming class, with the goal of determine solutions for linear problems using the Simplex method to the Travelling Salesman Problem.

The Travelling Salesman Problem

A salesman needs to make sales in some cities in the State of Minas Gerais (Brazil):

• Belo Horizonte
• Governador Valadares
• Juiz de Fora
• Montes Claros
• Uberlândia

➡️ His path will start in Belo Horizonte.
➡️ To minimize travel costs, the salesman needs to establish the best route for circulation between cities.
➡️ The displacement between cities will be carried out by road transport.

Thus, the costs of tickets between cities were collected:

	Belo Horizonte	Governador Valadares	Juiz de Fora	Montes Claros	Uberlândia
Belo Horizonte	-	63.60	53.20	90.40	159.40
Governador Valadares	63.60	-	90.80	106.8	169.40
Juiz de Fora	53.20	90.80	-	135.40	157,60
Montes Claros	90.40	106.8	135.40	-	125.40
Uberlândia	159.40	169.40	157,60	125.40	-

Symmetric matrix

The traveling salesman needs to establish a route that allows him to visit all the cities only once at the lowest cost of transfer and at the end, return to the initial city.