Creating index formula to find the Min value and heading with parameters

My question is in the sheet I have provided I have relevant destination from point"A" to point "B" to meet the parameter (Weight) to match the job(Mode type) and the relevant cost (Min cost) and will need to find the heading (The Min Value supplier) that the value was found under. I tried the Index, Match, IF formulas to find a solution however it is too complicating since there is too many variables involved. If there is other ways doing this problem please advice. I have attached a sample file.

So if weight is 34000 then its best to hire a B/double load and its cheapest provider in the pool is EE company B/Double Load so the AS column should provide answer "EE B/Double Load". If weight is more than 34,000 then It needs to provide two providers with the relevant other option as well.

Hi Bebo,
Thank you for your response on this question it works for the given parameters I'll workout how to find when there is a need for additional mode type when weight is above 40,000. Thank you