Use the following references below to solve a$,$b$,$ and c using the image to guide the problem.

For a reference LWR: assume a thermal efficiency is $33\%,$ power $1150$ MWe, uranium is $$70/$lb$.$ U$3$O$8,$ SWU is $$120/$kgSWU$,$ conversion is $$40/$kgU$,$ fabrication costs are $$400/$kgU$,$ losses in conversion $0\mathrm{.}15\%,$ losses in fabrication $0\mathrm{.}1\%,$ tails assay of $0\mathrm{.}2$wt$\%,$ reference core contains $90$ tonne fuel with enrichment of $4\mathrm{.}2\%.$ An average economical grade of uranium ore is $0\mathrm{.}2\%.$ Each fuel assembly contains $500$kg of fuel. The reactor operates on a $3-$batch equilibrium cycle of $18$ months which includes $17$ months at power including $3-$day startup and $1$ day for shutdown.

Data for recycling and disposal: Price of reprocessing $($$$/$kg used fuel$)=1000,$ Price of MOX fabrication $($$$/$kg$)=500,$ Price of DU $($$$/$kg$)=5,$ used fuel is $0\mathrm{.}93$ kg used fuel$/$kg fresh fuel, used fuel has $6\mathrm{.}0$ g fissile Pu$/$kg used fuel, fissile Pu has a reactivity equivalency of $0\mathrm{.}8$ g U$235$equivalent$/$g fPu$),$ loss in reprocessing$=0\mathrm{.}005$; losses in fabrication same as UO$2$ fuel; Table $1$ shows information on reactor grade plutonium; dry casks can hold $32$ spent fuel assemblies and costs $$1\mathrm{.}2$M to purchase and load.

Financial$/$economic data: annual interest rate is $4\%,$ interest is compounded monthly

Assume the average home requires an electrical power of $1\mathrm{.}2$kW with only power from nuclear energy. Suppose the average home occupancy is $2\mathrm{.}8$ persons and an average life expectancy of $75$ years. Utilize data for the reference LWR$.$

a$.$ What would be the lifetime uranium resource requirement per person without recycling?

b$.$ What would be the lifetime generation of vitrified high$-$level waste $($HLW$)$ per person in kg and liters $($assuming reprocessing and recycling of U and Pu$).$ Recall from your lecture notes and handouts for chapter $7,$ the vitrified waste containers in France weigh $480$kg and hold the HLW equivalent of $1\mathrm{.}5$ recycled fuel assemblies.

c$.$ Using the comparison of the life cycle carbon emissions for different technologies in terms of grams Carbon equivalent per kWhe $($from introductory slides for Chapter $1)$ and assuming a carbon tax of $$25/$t CO$2,$ what would be the per person lifetime savings $($in carbon taxes$)$ afforded by the referenced nuclear plant per year over an equal production of electricity by coal? By

natural gas? Read average values from below as: Nuclear: $4$ gCO$2\_$eq$/$kWhe $($read as grams CO$2$ equivalent per kWhe$),$ Coal: $300$ gCO$2$eq$/$kWhe$,$ Natural gas: $195$ gCO$2$eq$/$kWhe