Using Max and Sumif together

Hi,

I need to find a formula in order to find the name of the sector with the highest fee. Please see the enclosed sample file. I have also stated the expected outcome in the same file. I understand this could be done with Max and Sumifs formula but cant figure it out.

What i need is to have the name of the sector against a person for which his combined fee is maximum. Ex: since ABC has worked for 2 sectors (A&M and C&M) but his max fee is in C&M, so his sector with max fee should be C&M. Similarly for NBF, the sector with max fee should be AED as his fee add up to 30 as against A&M with a fee of 20. Also, if only 1 fee is there then it should take that as max and throw the sector. Such is the case of FGH.

Can anyone please help?

Or try this regular formula in F3

Formula:

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Or in another way

Formula:

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