Add rows in Alternate columns, divide by fixed rate per column.

Sorry if my descriptive title falls short, wasn't sure how to phrase it.

In the attached I have about 40 columns of data. Each line has a different month. Each Column is either IVE Eligible or NonIVE Eligible. Under each column there's a rate, that is then multiplied by the total for each column to arrive at a cost per each column.

If there's a disconnect between the final dollar amount I arrive at, as compared to my source documents, I have to find which month(s) the error falls in. That's the purpose of the little table in AQ:AU.

My formula's in AR:AS are what I would like some help with. Currently I'm using a ridiculously long formula, which I'd like to simplify. However, I'm not allowed to change the structure of the A:AP table. I tried multiplying the total IVE by the Average IVE rate but that doesn't calculate correctly. Any help on this would be appreciated.