The probability that the majority of a three-person jury will convict a guilty person is given by the formula: P(r, s, t) = rs(1 - t) + (1 - r)st + r(1 - s)t + rst subject to the constraint that r + s + t = α, where r, s, and t represent each of the three jury members’ probability of reaching a guilty verdict and a is some fixed constant that is generally less than or equal to the number of jurors.

(a) Form the Lagrange function.
(b) Find the values of r, s, and t that maximize the probability of convicting a guilty person when α = 0.75.
(c) Find the values of r, s, and t that maximize the probability of convicting a guilty person when α = 3.