This paper revisits an observation made in Wright (2012) which states, "We present a surprising though obvious result that seems to have been unnoticed until now. In particular, we demonstrate the equivalence of two well-known problems—the optimal allocation of the fixed overall sample size n among H strata under stratified random sampling and the optimal allocation of the n = 435 seats among the H = 50 states for apportionment of the U.S. House of Representatives following each decennial census... We give explicit exact solutions for both and note that the solutions are equivalent." The optimal exact sample allocation is essentially always an improvement over Neyman (1934) allocation, which generally requires rounding; this rounding jeopardizes the claim of minimum variance for Neyman allocation. In this paper, we reverse the approach and explicitly state and solve one simple general problem in its purest mathematical form. As a consequence of this general problem, we show explicitly that both exact solutions, noted above for apportionment and stratified sampling, follow immediately. A supplementary report provides detailed computations for official data and apportionment of the House following the 2020 Census of the USA. We also state and solve another simple general problem in its purest mathematical form.