The G $-$ Lab Company produced three joint products at a joint cost of $$150,000.$ Two of these products were processed further. Production and sales were:

$\backslash$table$[[$Product$,$Weight,Sales,Additional$],[$Processing Costs,,,,$],[$A$,400,000lbs,245,000,200,000,],[$B$,500,000lbs.,30,000,0,],[$C$,600,000lbs.,175,000,100,000,]]$

If joint costs are allocated based on relative weight of the outputs and all products are main products, how much of the joint costs would be allocated to product $A?($Do not round intermediary calculations. Round final answer to the nearest cent.$)$

A$.$ $$81,666\mathrm{.}67$

B$.$ $$60,000\mathrm{.}00$

C$.$ $$100,000\mathrm{.}00$

D$.$ $$40,000\mathrm{.}00$