Please help me find a correct formula using multiple sheets

I have different customers quoted with different rates. I need to chosse the cheapest rates and identify the customer's name along with the rate.

Please help me find a correct formula to display the customer’s name with cheapest rates located in the sheet tabs. See attached.

Sheet tabs are:

Main: Formula to be enter
Customer1: Carlo
Customer2: Mark
Customer3: Anthon

Advance thanks!

***************************************************************************************************

But I do hope below will clarify more, let me know if still unclear.

'cheapest rates' under 'Main' tab sheet will be the input and the Customer Name/s header will be the ouput.
Cheapest Rates column is the result of the minimum amount from Customer1, Customer2 and Customer3 sheet tabs.
Basically I need to identify the specific customer name/s of the cheapest rates.

Thanks

This seems pretty easy,But, until we know where to match a name(and how..!), it's sort of hard...Where does the Matching Customer Name come from?
In other words, where's the input to match the output to?

I understand that is a sample workbook, but why not put all data onto the same sheet? that will have summaries much simpler

Okay, I have come up with this:
Consolidation.xlsx
I won't post all the formulas here, there are many
But, I will explain a bit, I've created a new sheet called DATA, then created some named ranges from the produced data, then used this to give you a drop down list in MAIN D1:F1 (normally I would suggest getting rid of the merged cells, but, in this case, it is actually better for them to be merged , I did, however, unmerge A1:C1 and center across selection)
the cells in D3:F3 use the data in 'DATA' to determine which sheet to get the information from
(NOTE: This particular solution only works with the sheet naming convention used in the example (if you change the sheet names, it fails unless you change the formulas as well)

Hope this helps