What Function to use to get the minimum cost of selecting one of several groups of costs

[nrowe]

Sorry if the title is confusing, I'm not sure how to describe it. Basically, I need some homework help. The table is costs related to airplane tickets from and to different cities. The problem states that I have to start and end in new York, one of the 6 cities, and must visit each of the other cities once in a complete tour, and to figure out the lowest cost tour. How do I figure out this value? It can't be calculated from a single row or column, as you could go from city 2, to city 5, to city 3, etc. How do I find the optimal cost given multiple rules? If possible, only use the EXP, LN, MAX, MIN, SQRT, SUM, SUMPRODUCT, INDEX, MATCH, VLOOKUP, IF, AND, OR functions, as those are the ones the book describes in the chapter.
Please give me as much help as you can, I'm totally stumped.

 

[Special-K99]

Here's my shot at it.

You have to visit each of the cities only once.
So first you have 6 cities to visit then 5 then 4 then 3 etc
Therefore there are 6! = 720 possibitlities.

I would generate a table of all 720 possible routes and find the minimum of that.
I suspect you have a predefined table within the question telling you of the cost between each city from one to another, presumably a 6x6 table ?

So if you start off from city 1 to city 2 just sum the cost from the predefined table between cities 1 and 2, then the next two cities 2 and 3 etc
Obtain a total for the route then just use MIN()