Use the following reference 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.

Evaluate an enriched UO$2$ fuel for the reference LWR:

a$.$ What would be the cost per kg of the fabricated UO$2$ fuel?

b$.$ Now, considering the time value of money, calculate the cost of the fuel $($$$/$kg$)$and the cost of a fuel reload to the point it is loaded in the reactor for operation assuming you purchase in advance: uranium $48$ months, conversion $36$ months, enrichment $24$ months, and fabrication services $18$ months.

c$.$ Accepting the US resource data $($Identified Resources: $4,688,068$ tonnes RAR and $3,229,387$ tonnes IR$)$ from the $2020$ OECD Red Book, how long could you fuel the$93$ current reactors in the US$?$ Assume each has the same parameters as the reference LWR$.$ Be sure to clearly state the resource values you are referencing in this calculation and provide the reference.