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Default complicated problem I think Excel can handle

I have groups of rows with first cell identifying the group and the rest have
values like:
part1 10 8 11
part1 9 4 15
part2 13 14 6
part2 3 15 7

total 23 22 17

I need Excel to select the set of parts that will produce the highest values
when each parts values are added to the corresponding values of the other
parts. As in my example the first part1 and part2 were selected to yield the
total 23 22 17. In reality there will be 6 or more parts with 5 values each
and 50 or more of each part to select from.
 
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