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

and ???????? (i.e., ???????? −????????), suppose the goal is to minimize the total cost of sampling for a fixed value of the bound on the error of estimation. Determine the overall sample size ???? and the individual sample sizes ???????? and ????????, when

(a) ???? = 2.5, ????̇ ???? = 20, ????̇ ???? = 15, ???????? = $5, and ???????? = $4.

(b) ???? = 10, ????̇ ???? = 300, ????̇ ???? = 400, ???????? = $10, and ???????? = $5.