  We analyze 9.7 x 10^6 B\bar{B}$ pairs recorded with the CLEO detector to
determine the production ratio of charged to neutral B-meson pairs produced at
the Y(4S) resonance. We measure the rates for B^0 -> J/psi K^{(*)0} and B^+ ->
J/psi K^{(*)+} decays and use the world-average B-meson lifetime ratio to
extract the relative widths f+-/f00 = Gamma(Y(4S) -> B+B-)/Gamma(Y(4S) ->
B0\bar{B0}) = = 1.04 +/- 0.07(stat) +/- 0.04(syst). With the assumption that
f+- + f00 = 1, we obtain f00 = 0.49 +/- 0.02(stat) +/- 0.01(syst) and f+- =
0.51 +/- 0.02(stat) +/- 0.01(syst). This production ratio and its uncertainty
apply to all exclusive B-meson branching fractions measured at the Y(4S)
resonance.
