. Human blood types are classied by three gene forms A, B, and O. Blood types AA, BB, and OO are homozygous, and blood types AB, AO, and BO are heterozygous. If p, q, and r represent the proportions of the three gene forms to the population, respectively, then the Hardy-Weinberg Law asserts that the proportion Q of heterozygous persons in any specic population is modeled by Q(p, q, r) = 2(pq + pr + qr) subject to p + q + r = 1. Find the maximum value of Q.