Formula To Lookup and Sum cells together based on another cell

Hi guys I'm trying to figure out a formula that would Lookup data in an array and have it SUM with other data based on what's typed in a cell.
ie in the attachment file if cell A7 had 1 or more thing typed in it then cells C10:C15 would LOOKUP the data array in AB36:AH36 (more data will be inputted later) and do a Sum with the appropriate cells found in M1:Q1 and have the total in the proper place. I know I might have to do a formula for each cell in the C10:C15 array to work but thats ok. Also I know that some cells in M1:Q1 have a #NAME error I had to delete alot of the Ref in the Name Manager to slim down the file size to attach it. The info in there is good on the original.

Please help.

Is doing this even possible