= Solution
<burnup> refers to thermal energy per initial heavy-metal mass. Correct the electrical rating for <thermal efficiency> before using it, and apply the <capacity factor> once:
$$
P_{\rm th}=\frac{1600}{0.33}=4848.48 \mathrm{MW},\qquad
E_{\rm th}=P_{\rm th}(365)(0.9)=1.592727\times10^6 \mathrm{MW\,d\,yr^{-1}}.
$$
Consequently the annual initial heavy-metal fuel requirement is
$$
M=\frac{E_{\rm th}}{45000}=\boxed{35.394 \mathrm{t\,HM\,yr^{-1}}}.
$$
Let $F,P,W$ be feed, enriched product and <enrichment tails> masses, all measured as <uranium>, and $x_f,x_p,x_w$ the corresponding <uranium-235> <mass fractions>. The <isotopic mass balance> gives
$$
F=P+W,\qquad Fx_f=Px_p+Wx_w,\qquad
\frac FP=\frac{x_p-x_w}{x_f-x_w}=\frac{0.040-0.003}{0.007-0.003}=9.25.
$$
With $P=M$, the <uranium oxide concentrate> requirement is therefore
$$
F=9.25M=\boxed{327.394 \mathrm{t\,U\,yr^{-1}}},\qquad W=292.000 \mathrm{t\,U\,yr^{-1}}.
$$
These are <uranium> or heavy-metal masses, \b[not tonnes of <uranium> oxide]. The check $327.394(0.007)=35.394(0.040)+292.000(0.003)$ closes the <uranium-235> balance as well as the total mass balance.
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