In developing a sampling plan for estimating the difference between the means ????????

and ???????? (i.e., ???????? − ????????), suppose the goal is to minimize the overall sample size ????.

Determine the overall sample size ???? and the individual sample sizes ???????? and ????????, when

(a) ???? = 5, ????̇ ???? = 40, and ????̇ ???? = 50.

(b) ???? = 45, ????̇ ???? = 200 and ????̇ ???? = 250.

(c) ???? = 0.25, ????̇ ???? = 2 and ????̇ ???? = 1.5.