Use Lagrange multipliers to solve the following exercise. Common blood types are determined genetically by three alleles A, B, and O. (An allele is any of a group of possible mutational forms of a gene.) A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous. The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is P(p, q, r) = 2pq + 2pr + 2qrwhere p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population. Use the fact that p + q + r = 1 to show that the maximum proportion of heterozygous individuals in any population is 2/3?