A property title search firm is contemplating using online software to increase the productivity of the researcher performing the search. Currently, an average of $59$ minutes is needed to do a title search. The researcher cost is $$1\mathrm{.}30$ per minute. Clients are charged a fee of $$400.$ Company A$$s software would reduce the average search time by $16$ minutes, at a cost of $$3\mathrm{.}60$ per search. Company B$$s software would reduce the average search time by $17$ minutes at a cost of $$5\mathrm{.}60$ per search.

a$.$ Calculate the productivity in terms of revenue per dollar of input. $($Round your intermediate calculations and final answers to $2$ decimal places.$)$