How can we see on the Master table, the cheapest company from the Details Table?

I'm going to assume you have 3 tables in this set up.

(1) Products
(2) Vendors

and the joined table of call it (3) Product Sources

Each vendor & each product will have many product sources.

Then you can enter the prices for each supplier on the items.  Then you can summarize the cheapest supplier cost.  And really do anything else you need to.

If you need more details let me know.

First thanks for your help 

Your assumption was good, we have 3 Tables, but I want the cheapest Supplier NAME to show up in the products table, not the Cheapest PRICE

Can this be done?

if you use the summary field  pull over the Record ID of the cheapest supplier cost, you can set up a separate relationship based on that RecordID and pull over whatever from that record.

might be a simpler way to go, but it works for us 'mere mortals'. :)

Yep, you are on the right track.  

You will need to summarize the cheapest PRICE first,
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then send that price back down to the joined table as a lookup field
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Then summarize the minimum Record ID# with the condition of [Price] is equal to the value in the field [New summarized lookup price field].  Say its something like [Cheapest Joined Record ID#]

This will give you the record ID# for that joined record.
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Then ( you create something that I really don't like doing, but for this case it might be the best option)  you create a reverse relationship.
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Each "Joined Table Record" will have many "Products", but for the field of the relationship be sure to use the [Cheapest Joined Record ID#]
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then you can pass the name, and any other information as lookup fields to the Product table.

Is this method called "reverse relationships"?

Why is the reason that you don't like to do the reverse relationship?

What are the disadvantages?

Thank you for your help, it's it's working excellent