Optimal data from table

Hi There folks,
(attached file)

i have this table with scores each brand gives me, and i need to reach the maximum score.
from each position i can take only one score (one brand).

what i know is to take the highest score from each position (the left table in the file attached), but the optimal is to take 2nd option (the table on the right).
the problem is i have big tables and i need the excel to calculate the optimal score (like in the table on the right).

can it be done easily (calculate all the options and find the best optimal score)?

thank you...

How many brands and how many positions?

50 Brands & 10 Positions

...that is a large number of combinations!!!!

Perhaps one of the forum mathematicians can suggest an "optimising" algorithm rather than a brute force approach of trying all combinations.