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.