= Solution
The recycle feed is the recovered <uranium>, not the whole initial <nuclear fuel> charge. After the stated loss it is
$$
F_r=27(1-0.015)=26.595\ \mathrm{t\,U\,yr^{-1}}.
$$
Using the same <enrichment tails> assay and the stipulated higher recycle-product assay, the <isotopic mass balance> gives
$$
P_r=F_r\frac{0.0085-0.003}{0.053-0.003}
=2.925450\ \mathrm{t\,U\,yr^{-1}},\qquad
W_r=F_r-P_r=23.669550\ \mathrm{t\,U\,yr^{-1}}.
$$
Treat the $5.3\%$ recycled product as replacing the same <uranium> mass of ordinary $5.0\%$ <nuclear fuel>: the additional <uranium-235> compensates for the supplied <uranium-236> penalty. It displaces fresh natural-uranium feed in the ratio calculated in part (b), hence
$$
\Delta F=11.75P_r=\boxed{34.37404\ \mathrm{t\,U\,yr^{-1}}}.
$$
The remaining natural feed is $313.36245\ \mathrm{t\,U\,yr^{-1}}$, a \b[9.885% resource saving] relative to the full-power once-through requirement. This credits one <uranium> recycle only; it adds no second-pass recycling or <plutonium> credit.
Separative work must be charged for producing the recycled <nuclear fuel> as well as credited for displaced fresh <nuclear fuel>. With <uranium-235> <mass fraction> $x$, use the <separative value function>
$$
V(x)=(1-2x)\ln\frac{1-x}{x},\qquad
S=PV(x_p)+WV(x_w)-FV(x_f).
$$
Masses in kilograms give work in kg-SWU. For ordinary fresh product the work per product kilogram is
$$
s_f=V(0.050)+10.75V(0.003)-11.75V(0.007)
=7.28741475\ \mathrm{kg\!\text{-}\!SWU\,kg^{-1}}.
$$
Thus the fresh work avoided is
$$
S_{\rm avoided}=1000P_rs_f=21318.9675\ \mathrm{kg\!\text{-}\!SWU\,yr^{-1}}.
$$
The recycled product still requires
$$
S_r=1000\big[P_rV(0.053)+W_rV(0.003)-F_rV(0.0085)\big]
=19726.2085\ \mathrm{kg\!\text{-}\!SWU\,yr^{-1}}.
$$
The \b[net separative-work saving] is consequently
$$
\Delta S=S_{\rm avoided}-S_r
=\boxed{1592.7590\ \mathrm{kg\!\text{-}\!SWU\,yr^{-1}}}.
$$
As a whole-cycle check, the fresh route requires $215668.0851$ kg-SWU per year, while the mixed fresh-plus-recycled supply requires $214075.3261$ kg-SWU. The net saving is only \b[0.7385%] of the original work. The recovered stream has a higher <uranium-235> assay than natural feed, but the higher required product assay uses most of the work credit. These equations are resource accounting and do not specify an <uranium enrichment> plant or its operation.
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