Need formula to draw out minimum values

Hi all
I've attached a copy of what I am looking for
Table 1 is where I would put in the information I have obtained from carriers on their cost for particular lanes.
I filled in Table 2 with what I want the table to display, but what I am loooing for are formulas to automatically draw form table one and fill in the same information.
I want Table 2 to display no duplicate lanes ( only show "Origin A" and "Destination A" once) and then to display the minimum cost associated with that lane ("Carrier A" charges $500, "Carrier B" charges $100, display $100).
I am sure there is a way to do this, just can't figure it out for the life of me. If I need to make a helper column that is not ideal, but can be done.
Any help would be much appreciated!
Thanks in advance.

Not quite sure about the Formula,but you can do this by using Sort and Advance Filter.First Sort the Cost then use Select the Origin & Destination Column Apply Advance Filter,checked unique record only..

You will get your desired result

Thanks for the help dan.
I really wanted the table to autofill, and was finally able to use a formula I got from another forum Thread to draw out unique values from a list.
I typed the following explanation up before I finally realized how to attach the file to this reply, so either read below or view the file to see how I accomplished this.

First I inserted two columns in front of column C.
I inserted the following formula in D10 and dragged down:

Formula:

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I inserted the following formula in C55 and dragged down (don't ask me how it works... I just copied it off of another forum. Make sure to use Shift-Ctrl-Enter!):

Formula:

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I used vlookup formulas in column E and G for Table 2:

Formula:

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and

Formula:

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respectively.
I finally used this formula in cell I55 and dragged down (Shift-Ctrl-Enter!):

Formula:

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I think it will work perfectly!