I am trying to create a formula that would return the smallest sum value for each color.

For example, in the table below amount 01 and amount 02 are added together. The results I am looking for would be Green 6, Blue 8, and Red 11.

Color Amount 01 Amount 02
Green 1 5
Blue 6 2
Red 5 6
Green 8 2
Red 7 7

I am trying to avoid having a total column in each row or using macros. Is there a way to do this with just formulas?