Problem:
Captain America (Cap) is transported by one of his foes to the planet Trellis, where he is forced to participate in gladiatorial games with the native Trellisians. While no one is severely injured during these battles, winners do get an extra piece of Trellisian apple pie for dessert.
The size of Cap's opponents is determined by alleles at seven loci in the Trellisian genome: we shall label them A1, a1, A2, a2, ..., A7, a7. Each capital allele is an increaser allele, adding the same amount to the size and weight (musculature) of the Trellisian competitor, and each lower-case allele is a null allele, adding nothing.
Cap knows that the smallest opponent he has faced, who is homozygous for all lower-case alleles, has a Trellisian Musculature Index (TMI) of 56. Cap also knows that his 2nd opponent, with a multi-locus genotype of:
A1a1 a2a2 a3a3 A4A4 A5a5 a6a6 A7a7,
has a TMI of 181.
Required:
Question: Given this information, what is the TMI of the strongest opponent Cap must face; that is, the opponent who is homozygous for all capital alleles at all seven loci?
A.225.
B.406.
C.356
D.381.
E.431.
Please give reasoning with your answer.